Three cubes whose edges measure 3cm,4cm,5cm respectively to form a single cube.Find its edge.Also find the surface area of the new cube.
Volume of new cube = Sum of volume of three cubes
= 33 + 43 + 53
= 216 cm3
i.e., (edge)3 = 216 cm3
So, Edge of the single cube = 6 cm
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Given : Three cubes of metal with edges 3 cm, 4 cm and 5 cm are melted to form a new single cube
Let the edge of new cube be a.
⇒ Volume of new cube = Volumes of three small cubes
⇒ a 3 = (3 cm)3 + (4 cm)3 + (5 cm)3
= a3 = 27 cm3 + 64 cm3 + 125 cm3
= a3 = 216 cm3
⇒ a = 6 cm
Hence Lateral surface area of new cube = 6a 2
= 6 x (6 cm)2 = 6 x 36 cm2
= 216 cm2
- 2
Given : Three cubes of metal with edges 3 cm, 4 cm and 5 cm are melted to form a new single cube
Let the edge of new cube be a.
⇒ Volume of new cube = Volumes of three small cubes
⇒ a 3 = (3 cm)3 + (4 cm)3 + (5 cm)3
= a3 = 27 cm3 + 64 cm3 + 125 cm3
= a3 = 216 cm3
⇒ a = 6 cm
Hence Lateral surface area of new cube = 6a 2
- 3
Second edge= 4 cm
Third edge = 5 cm
VOLUME OF NEW CUBE = SUM OF VOLUME OF ALL THREE CUBES
VOLUME = A3
V1= 33
V2=43
V3=53
V1+V2+V3=VOLUME OF NEW CUBE
27+64+125= 216cm3
Side of new cube = root of 216 (AS VOLUME = A3)
Side = 6 cm
EDGE = 6cm
TSA = 6a2
= 6*(6)2
= 6*36
= 216 cm2
TOTAL SURFACE AREA = 216 CM2 EDGE = 6 CM
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- 4
To form a single large cube,
The total volume of all small cubes= 33+43+53=27+64+125=216 cm3
So the edge of the larger cube is= 2161/3=6 cm
The total surface area of the larger cube is=6x2=6*36=216 cm2
Hence, the larger cube has a surface area of 216 cm2
- 3
a^3 + b^3 + c^3 = x^3 .........( where x is edge of greater cube and a,b,c are edge of smaller cube)
3^3 + 4^3 + 5^3 = x^3
9+64+125 = x^3
216 = x^3
(6)^3 = x^3
on comparing x will equal to 6
so, edge of greater cube is equal to 6
Surface Area will equal to 6a^2
6 x (6)^2
216 cm^2
- 0
Volume of 1st cube = edge^3
=3^3
=27cm^3
Edge of 2nd cube=4cm
Volume of 2nd cube =4^3
=64cm^3
Edge of 3rd cube =5cm
Volume of 3rd cube =5^3
=125cm^3
Total volume of the 3 cubes =Volume of new cube
Volume of new cube = 27 +64+125cm^3
=216cm^3
Edge^3=216
Edge=6cm
Surface area of the new cube = 6×edge^2
=6×6^2
=216cm^2
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