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Syllabus

a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis , parallel to its base . compare the volume of the two parts

In triangle ABC, AB = 20, AC=15, BC=7Line segment BC is extended past C to D so that triangles DAB and DCA are similar. Find DC.

a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?

A well of diameter 3m ,dug 14m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment.

a warehouse is used as a granary. is is the shape of a cuboid surmounted by a half-cylinder. the base of the shed is 6m x 14m and its height is 8m. find the surface area of the non-cubiodal part.

The height of a cone is 30cm.A small cone is cut off at the top by a plane parallel to the base.If its volume be 1/27 of the volume of the given cone,then what is the height above the base at which the section is made?

water is flowing at the rate of 15km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50m long and 44m wide . find the time in which the level of water in the tank will rise by 21 cm

Plz exlain me the relation between litre ans cm

^{3}and m^{3}.A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, find the ratio of the line segments into which the cone's altitude is divided by the plane.

a cylinder , a cone and a hemisphere of equal base have the same height. what is their ratio in their volumes ?

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes>

A hemispherical tank , full of water , is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m ?

all surface area volume chapter's formulas

A cone of maximum size is carved out from a cube of edge 14cm . FInd out the surface area of the cone and of the remaining solid left out after the carved out . Plzz Answer ....

height 14 cm is dipped vertically one third in a

bucket full of paint. How much area gets painted?

A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypoteneous.Find the volume and the surface area of the double cone so formed. (Take pie = 3.14

A toy in the shape of solid cylinder surmounted by a conical top.If the height of the diameter of the cylinder path are 21cm and 40cm respectively and height of the cone is 15cm.Find the total surface area of the toy. use pie=3.14

the rainwater from a roof 22m*20m drains into a cylindrical vessel having diameter of base 2 m and height 3.5m . if the vessel is just full , find the rainfall in cm.

pls do this problem in simple method

A cylindrical pillar of a temple is shown in the figure, which is conical at the top. Thereare 14 such pillars, in the temple. Find the cost of polishing their curved surface area at therate of ` 1.50 per m2.

total surface area of an hollow sphere and hemisphere?

If the diameter of a sphere is decreased by 25%, then by what percent its curved area would decrease?

if the semi vertical angle of a cone of height 3 cm is 60. find its volume.

the barrel fountain pen cylindrical in shape is 7cm long and 5mm in diameter. a full barrel of ink in the pen is used up in writing 330 words

on an average.

how many words would use up a bottle of ink containing one fifth of a litre?

CSA , TSA and volume of spherical shell

~Akash~

A sphere of diameter 12 cm is dropped in a right circular cylinder vessel partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 32/9cm. find the diameter of the cylindrical vessel.

cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. dm is rs.237.60 . the heigth of the tank is 6 times the radius of the base of tank . find its volume correct to two decimal point...? and is que. in easy

a copper wire 3mm in diameter ,is wound about a cylinder whose length is 12cm , and diameter 10cm so as to cover the csa of the cylinder . find the length and mass of the wire , assuming the density of copper to be 8.88g per cm3

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the TSA of the remaining solid.

a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100 cm

^{3 }( use pi= 22/7)if h,c,v are respectively the height, curved surface area and the volume of a cone.prove that

3 pie v h cube - c2h2 + 9v2 =0

A hemispherical depression is cut-out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

why are we subtracting in the base area as we know that CSA of hemisphere actually means the area of hemisphere without base

Already the base is excluded as we are adding only CSA of hemisphere then again y minus base area

I don't need answer just y need to add base area

What is the CSA, TSA and volume of a frustum?

find the square root of 13.625?

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14cm long, is 88cm2. If the volune of metal used in making the cylinder is 176cm3, find the outer and inner diameters of the cylinder

how can you find the surface area of a cube,cuboid,cone and a pyramid by using flat cut outs?

a sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water . the diameter of the cylindrical vessel is 12cm. if sphere is completely submerged in water by how much will the level of water rise?

A conical vessel of radius 6cm and height 8cm is completely filled with water. A spere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

a bucket i sin the form of frustum with the capacity of 12308.8 cm cube.the radii of the top and bottom of circular ends are 12 cm and 20 cm resp.find the hieght of the bucket and also the area of metal sheets used in making the bucket.(use pie=3.14)

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm??(please explain step-wise) :))Two cubes each of side 4cm are joined end to end.Find the surface area of the resulting cuboid

the diameter of internal and external surfaces of hollow sphercal shell are 6cm and 10cm respectively. if it is melted and recast into a solid cylinder of height 2

^{2}/3 cm.find the diameter of the cylinder?A well of diameter 3m, is dug 14m deep The earth taken out of it has been evenly spread all around it to a width of 4m, to form an embankment Find the height of the embankment use pi=22/7

the radii of the ends of the frustumof a cone 45cm high are 28cm and 7 cm. find its volume , the C.S.A & the T.S.A.

If the diameter of the cross section of the wire is decreased by 5%,how much %will the length be increased so that the volume remains the same

Q. A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. The whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.

the radii if the internal and external surface of a hollow spherical shell are 3cm and 5cm respectively. it is melted and recasted into a solid cylinder of diameter 14cm. find the height of the cylinder

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere (see figure). The diameters of the ends of the frustum are 5 cm and 2 cm , the height of the entire shuttle cock is 7 cm. Find the external surface area. (Take Pie=22/7) .

The curved surface area of a cylinder is 264 m

^{2}and its volume is 924 m^{3}. Find the ratio of its height to the diameter .From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm

^{2}.Given that,

Height (

h) of the conical part = Height (h) of the cylindrical part = 2.4 cmDiameter of the cylindrical part = 1.4 cm

Therefore, radius (

r) of the cylindrical part = 0.7 cmTotal surface area of the remaining solid will be

= CSA of cylindrical part + CSA of conical part + Area of cylindrical base

The total surface area of the remaining solid to the nearest cm

^{2}is 18 cm^{2}.Why C.S.A. of cone is added instead of subtracting(cause we have to find T.S.A. of remaining part)???

plz explain

The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8m, surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and volume of the building.

Shanta runs an industry in a shed which is in the shape of a cubeoid surmounted by half cylinder ..If the base of the shed is of demension 7m x 15m , and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold.Further, suppose the machinery in the shed accupies a total space of 300m

^{3}, and there are 20 workers each of whom ocupy about 0.08 m^{3}space on a average . Then how much air is in the shed?The height of right circular cone is trisected by two plane parallel to its base. Show that the volume of the three propotion from top are in ratio 1:7:19.

in example1 why is the tsa of remaining outer part = csa of cylinder + area of circle

or should it be = csa of cylinder - area of circle ??????

A swimming pool is filled by 3 pipes with uniform flow, The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the 3

^{rd}pipe alone. The 2^{nd}pipe fills the pool 5 hours faster than the 1^{st}pipe & 4 hours slower than the 3^{rd}pipe. Find the time required by each pipe to fill the pool separately.A solid cuboidal slab of iron of dimensions 66 cm x 20 cm x 27 cm is used to cast an iron pipe. If the outer diameter of the pipe is 10 cm and thickness is 1 cm, then calculate the length of the pipe.

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure).

t can be observed that

Radius (

r) of cylindrical part = Radius (r) of hemispherical part =Length of each hemispherical part = Radius of hemispherical part = 1.4 cm

Length (

h) of cylindrical part = 5 − 2 × Length of hemispherical part= 5 − 2 × 1.4 = 2.2 cm

Volume of one gulab jamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

Volume of 45 gulab jamuns == 1,127.25 cm

^{3}Volume of sugar syrup = 30% of volume

plz tell me why it is voulume of gulab jamun is taken to find the sugar suyrup. why we can't take area of gulab jamun in the place volume because container contain gulab jamun we can take their area and then the volume of container. im not able to understand the question. please try to explain with proper diagram.

Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m.In how much time will the cistern be filled? Also, plzz tell that here what is meant by cistern?????

A cylindrical copper rod of diameter 1 cm and length 8 cm is drawn into a cylindrical wire of length 18 m and of unifiorm thickness. Find the thickness of the wire.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m

^{2}. (Note that the base of the tent will not be covered with canvas.)A milk tanker, cylindrical in shape having diameter 2m and length 4.2m supplies milk to the boothes in the ratio 3:2. One of the milk booth has cuboidal vessel having base area 3.96m

^{2}and the other has a cylinderical vessel having radius 1m. Find the level of milk in each of the vesselsfind the area of the shaded region where ABCD is a square of side 14cm . ( four equal circle inside the square) . And please explain me how the radius is obtained .

Please solve the following question:

rnAn ice cream cone consiting of a cone is surmounted by a hemisphere. The common radius of the hemisphere and the cone is 3.5 cm and the total height of the ice cream cone is 12.5 cm. Calculate the volume of ice cream in the cone.

the derivatio of the formula of frustum of cone

two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14cm x 17 cm . Find the area of remaining card board?

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm

^{2}. [Take π = 3.14]in one fortnight of a given month ,there was a rainfall of 10cm in a river valley .if the area of the valley is 97280 km sq. ,show that the total rainfall was approx. equivalent to the addition to the normal water of the three rivers each ,1072 km long ,75m wide and 3m deep.

PLEASE HELP THIS ANSWER IS NOT AVAILABLE ON MERITNATION NCERT SOLUTION.

How to derive the formula for voulume of frustum of a cone?

- How to derive the relation bnetween the orginal cone radius / height to the portion of the cone that is removed?

Water is flowing through a cylindrical pipe, of internal diameter 2cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour.

Two squares are inscribed in a semicircle as shown in the figure. If the area of the smaller square is 25 sq. units, then what is the area of the larger square?

(A) 100 sq. units

(B) 50 sq. units

(C) 225 sq. units

(D) 400 sq. units

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream

A solid toy is in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2cm and the diameter is 4cm. If a right circular cylinder circumscribes the solid,find how much more space it will cover.

two solid cones A and B are placed in acylindrical tube. the ratio of their capacities are 2:1. find the heights and capacities of cones. also find the volume of the remaining portion of the cylinder.