NCERT Solutions 10th Maths Chapter 13 Surface Areas and Volumes Exercise 13.1

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Exercise 13.1
1. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Solution:
Let the length of side of the cube be a cm.
Then, its volume = a3 cm3 ⇒ a3 = 64 [Given]
⇒ a = ∛64 = 4 cm
By joining the two cubes, a cuboid is formed withe length, breadth and height 8 cm, 4 cm and 4 cm respectively.
∴ Surface area of the cuboid = 9(lb + bh + hl)
= 2(8 x 4 + 4 x 4 + 4 x 8) cm2
= 2(32 + 16 + 32) = 160 cm
2.A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Solution:
Radius of hemisphere, r = 14/2 =7 cm
Height of cylinder, h = 13 - 7 = 6 cm