R.d Sharma 2022 Mcqs Solutions for Class 9 Maths Chapter 18 Surface Area And Volume Of A Cuboid And Cube are provided here with simple step-by-step explanations. These solutions for Surface Area And Volume Of A Cuboid And Cube are extremely popular among class 9 students for Maths Surface Area And Volume Of A Cuboid And Cube Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 Mcqs Book of class 9 Maths Chapter 18 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 Mcqs Solutions. All R.d Sharma 2022 Mcqs Solutions for class 9 Maths are prepared by experts and are 100% accurate.

Page No 190:

Question 1:

The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is

(a) 10 cm

(b) 102 cm

(c) 103 cm

(d) 20 cm

Answer:

The longest rod that can be fitted in the cubical vessel is its diagonal.

Side of the cube

So, the diagonal of the cube,

So, the length of the longest rod that can be fitted in the cubical box is.

Hence, the correct choice is (c).

Page No 190:

Question 2:

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

Answer:

Let, Side of each cube

So, the dimensions of the resulting cuboid are,

Length

Breadth

Height

Total surface area of the cuboid,

Sum of the surface areas of the three cubes,

Required ratio,

Thus, the required ratio is.

Hence the correct choice is (a).

Page No 190:

Question 3:

If the length of a diagonal of a cube is 83 cm, then its surface area is

(a) 512 cm2

(b) 384 cm2

(c) 192 cm2

(d) 768 cm2

Answer:

Let,

Side of the cube

Length of the diagonal

We have to find the surface area of the cube

Surface area of the cube,

Thus, surface area of the cube is.

Hence, the correct choice is (b).

Page No 190:

Question 4:

If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is

(a) 8 : 1

(b) 22:1

(c) 2 : 1

(d) none of these

Answer:

Let,

Volumes of the two cubes

Edges of the two cubes

We know that,

So,

Ratio of their edges is.

So, the correct choice is (c).

Page No 190:

Question 5:

The volume of a cube whose surface area is 96 cm2, is

(a) 162cm3

(b) 32 cm3

(c) 64 cm3

(d) 216 cm3
 

Answer:

Let,

Side of the cube

Volume of the cube

Surface area of the cube

We have,

So,

Thus, volume of the cube is.

Hence the correct choice is (c).

Page No 190:

Question 6:

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is

(a) 27 cm2

(b) 32 cm2

(c) 44 cm2

(d) 88 cm2

Answer:

Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.

So we can take,

We need to find the total surface area of the box

Volume of the box,

Thus,

Surface area of the box,

Thus total surface area of the box is.

Hence, the correct option is (d).

Page No 190:

Question 7:

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is

(a) 30 cm

(b) 20 cm

(c) 15 cm

(d) 10 cm

Answer:

Let, the edges of the cuboid be a cm, b cm and c cm.

And, a < b < c

The areas of the three adjacent faces are in the ratio 2 : 3 : 4.

So,

ab : ca : bc = 2 : 3 : 4, and its volume is 9000 cm3

We have to find the shortest edge of the cuboid

Since;

Similarly,

Volume of the cuboid,

As and

Thus, length of the shortest edge is.

Hence; the correct choice is (c).

Page No 190:

Question 8:

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

(a) 2 V

(b) 4 V

(c) 6 V

(d) 8 V

Answer:

Let, Initial edge of the cube

So,

In the new cube, let,

Edge of new cube

Volume of the new cube,

Volume of the new cube is.

Hence, the correct choice is (d).

Page No 190:

Question 9:

If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

(a) 2 S

(b) 4 S

(c) 6 S

(d) 8 S

Answer:

Let,

Length of the first cuboid

Breadth of the first cuboid

Height of the first cuboid

And,

Length of the new cuboid

Breadth of the new cuboid

Height of the new cuboid

We know that,

Surface area of the first cuboid,

Surface area of the new cuboid,

The surface area of the new cuboid is.

So, the correct choice is (b).

Page No 190:

Question 10:

The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is

(a) 60 dm3

(b) 600 dm3

(c) 6000 dm3

(d) 60000 dm3

Answer:

The area of the floor

Height of the room

We have to find the volume of the air in the room

So, capacity of the room to contain air,

Volume of the air contained in the room is.

So the correct choice is (d).

Page No 190:

Question 11:

The cost of constructing a wall 8 m long, 4 m high and 10 cm thick at the rate of Rs. 25 per m3 is

(a) Rs. 16

(b) Rs. 80

(c) Rs. 160

(d) Rs. 320

Answer:

Dimensions of the wall are,

Length

Breadth

Height

Volume of the hall,

Cost of building the wall at the rate of Rs. 25/m3,

The cost of building the wall is.

Hence, the correct option is (c).

Page No 190:

Question 12:

10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

Answer:

Volume of the clay to be spread,

Area on which the clay is spread

Let,

Rise in the level of the ground

We know that,

Rise in the level of the ground is.

Hence, the correct option is (a).

Page No 190:

Question 13:

Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is

(a) 24

(b) 48

(c) 72

(d) 96

Answer:

Let,

Length of the first cuboid

Breadth of the first cuboid

Height of the first cuboid

Volume of the cuboid is 12 cm3

Dimensions of the new cuboid are,

Length

Breadth

Height

We are asked to find the volume of the new cuboid

We know that,

Volume of the new cuboid,

Thus volume of the new cuboid is.

Hence, the correct option is (d).

Page No 190:

Question 14:

If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is

(a) 9

(b) 27

(c) 219

(d) 729

Answer:

A cube has total 12 edges.

Let, edge of the cube

Sum of all the edges of the cube = 12a

Volume of that cube,

Volume of the cube is.

Hence, the correct option is (b).

Page No 190:

Question 15:

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is

(a) 9

(b) 10

(c) 18

(d0 20

Answer:

We have the cuboid of dimensions.

We are to find how many cubs with edge 3 cm can be cut from the given cuboid

Let us cut this cuboid into following two cuboids

And

So the number of cubes of side 3 cm, that can be cut from the first cuboid,

We can not cut a single cube of side 3 cm from the second cuboid of dimension

Hence this much volume is useless for us.

So, we can cut maximum cubes of side 3 cm from the cuboid of dimensions.

Hence, the correct option is (c).

Page No 190:

Question 16:

On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

(a) 300 litres

(b) 450 litres

(c) 3000 litres

(d) 4500 litres

Answer:

Length of the terrace,

Breadth of the terrace,

Height of the water level

We have to find the quantity of water

Quantity of water,

The quantity of water is.

The correct option is (d).

 



Page No 191:

Question 17:

If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is

(i) A1 A2 A3

(ii) 2A1 A2 A3

(iii) A1A2A3

(iv) 3A1A2A3

Answer:

We have;

Here A1, A2 and A3are the areas of three adjacent faces of a cuboid.

But the areas of three adjacent faces of a cuboid are lb, bh and hl, where,

Length of the cuboid

Breadth of the cuboid

Height of the cuboid

We have to find the volume of the cuboid

Here,

Thus, volume of the cuboid is.

Hence, the correct choice is (c).

Page No 191:

Question 18:

If l is the length of a diagonal of a cube of volume V, then

(a) 3V = l3

(b) 3V=l3

(c) 33V=2l3

(d) 33V=l3

Answer:

We have,

Diagonal of the cube

Volume of the cube

Side of the cube

We know that,

So, the correct choice is (d).

Page No 191:

Question 19:

If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then AV

(a) x2y2z2

(b) 121xy+1yz+1zx

(c) 1x+1y+1z

(d) 1xyz

Answer:

Dimensions of the cuboid are.

So, the surface area of the cuboid

Volume of the cuboid

Hence, the correct choice is (c).

Page No 191:

Question 20:

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 55 cm. Its surface area is

(a) 361 cm2

(b) 125 cm2

(c) 236 cm2

(d) 486 cm2

Answer:

Let,

Length of the cuboid

Breadth of the cuboid

Height of the cuboid

We have,

, diagonal of the cuboid

We are asked to find the surface area

So, the surface area,

Thus, the surface area is

Hence, the correct choice is (c).

Page No 191:

Question 21:

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%

Answer:

Let,

Initial edge of the cube

Initial surface area of the cube

Increased edge of the cube

Increased surface area of the cube

We have to find the percentage increase in the surface area of the cube

Since it’s given that

We have,

Percentage increase in surface area,

Increase in surface area is.

Hence, the correct choice is (d).

Page No 191:

Question 22:

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

Answer:

Let,

Volumes of the three cubes

Sides of the three cubes

We know that,

So,

Similarly,

And;

So the height of the resulting structure,

The height of the structure is.

Hence, the correct choice is (a).

Page No 191:

Question 23:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If the lateral surface area of a cube is 100 m2, then its volume is 125 m3.
Statement-2 (Reason): If the lateral surface area of a cube is S, then its volume V is given by 64 V2 = S3.

Answer:


Statement-2 (Reason): If the lateral surface area of a cube is S, then its volume V is given by 64 V2 = S3.
Given that, the lateral surface area of a cube is S.

Let the side of the cube be a.
∴ S = 4a2
a=S4


Then volume of the cube (V) = a3
V=S4123V=S432V2=S43V2=S36464V2=S3

Thus, the correct Statement-2 is true.

Statement-1 (Assertion): If the lateral surface area of a cube is 100 m2, then its volume is 125 m3.

Given that, lateral surface area of a cube is 100 m2.

Now, according to the Statement-2.
64V2=S364V2=100364V2=1000000V=100000064V=10008V=125

Thus, the correct Statement-2 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Hence, the correct answer is option (a).









 

Page No 191:

Question 24:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If the volume of a cube is 125 cm3, then its lateral surface area is 100 cm2.
Statement-2 (Reason): The volume V and lateral surface area S of a cube are connected by the relation 64 V2 = S3.

Answer:

Statement-2 (Reason): If the lateral surface area of a cube is S, then its volume V is given by 64 V2 = S3.
Given that, the lateral surface area of a cube is S.

Let the side of the cube be a.
∴ S = 4a2
a=S4


Then volume of the cube (V) = a3
V=S4123V=S432V2=S43V2=S36464V2=S3

Thus, the correct Statement-2 is true.

Statement-1 (Assertion): If the lateral surface area of a cube is 100 m2, then its volume is 125 m3.

Given that, lateral surface area of a cube is 100 m2.

Now, according to the Statement-2.
64V2=S3641252=S364×15625=S31000000=S3100=S

Thus, the correct Statement-2 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Hence, the correct answer is option (a).

Page No 191:

Question 25:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If the areas of three adjacent faces of a cuboid are 12 cm2, 36 cm2 and 48 cm2 respectively, then its volume is 144 cm3.
Statement-2 (Reason): If the areas of three adjacent faces of a cuboid are x, y, z, then its volume V is given by V = xyz.

Answer:

Statement-2 (Reason): If the areas of three adjacent faces of a cuboid are x, y, z, then its volume V is given by V = xyz.

Let l, b and h be the length, breadth and height of the cuboid.
Then the area of the three adjacent faces of a cuboid will be lb, bh and hl.

Thus,
lb = x l=xb,  .....(1)
bh = y b=yh .....(2)
And hl = zl=zh  .....(3)
From (1) and (3),
xb=zhh=zbx              .....4
From (2) and (4),
b=yzbxb=xybzb2=xyz

Volume of cuboid (V) = lbh
=xb×yh×h=xyb
Thus, Statement-2 is false.

Statement-1 (Assertion): If the areas of three adjacent faces of a cuboid are 12 cm2, 36 cmand 48 cmrespectively, then its volume is 144 cm3.

Let lb and h be the length, breadth and height of the cuboid.
Then the area of the three adjacent faces of a cuboid will be lbbh and hl.

Thus,
lb = 12 l=12b                        .....(1)
bh = 36 b=36h                     .....(2)
And hl = 48 l=48h                      .....(3)

From (1) and (3),
48h=12b4b=h                 .....4

From (2) and (4),
b=364bb2=9b=3h=12l=4

Volume of cuboid (V) = lbh
=4×3×12=144 cm3

Thus, the correct Statement-2 is true.
So,  Statement-1 is true, Statement-2 is false.

Hence, the correct answer is option (c).







 

Page No 191:

Question 26:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If the surface areas of two cubes are in the ratio 25 : 16, then their volumes are in the ratio 125: 116.
Statement-2 (Reason): If S1, S2 are surface areas and V1, V2 are volumes of two cubes, then V1V2=S1S232.

Answer:

Statement-2 (Reason): If S1S2 are surface areas and V1, V2 are volumes of two cubes, then V1V2=S1S232

Let a1 and a2 be the sides of two with surface areas S1 and S2 respectively and volumes V1 and V2 respectively.

So,

V1V2=a13a23V1V2=a1a23V1V213=a1a2                             .....1

Now,
S1S2=6a126a12S1S2=a12a22S1S2=a1a22S1S2=V1V2132               From 1S1S2=V1V223S1S23=V1V22V1V2=S1S232

Thus, Statement-2 is true.

If the surface areas of two cubes are in the ratio 25: 16, then their volumes are in the ratio 125 : 116.

Let S1 and S2 be the surface areas of two cubes respectively and volumes V1 and V2 be the volumes of two cubes respectively.

Here,  S1 : S2 = 25 : 16

Now, according to Statement-2 
25163=V1V2252423=V1V225423=V1V22546=V1V22543=V1V212564=V1V2
⇒ V1 : V2 = 125 : 64
Thus, Statement-1 is false.

So, Statement-1 is false, Statement-2 is true.

Hence, the correct answer is option (d).



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