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Class 10

Chapter 13 - Surface Areas and Volumes

Exerise 13.2

22

Unless stated otherwise, take n = —.

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1.    A solid is in the shape of a cone standing on a hemisphere with both their mdii being eąual to 1 cm and the height of the cone is eąual to its radius. Find the oolume of the solid in terms of n.

Sol. Volume of the solid

= volume of the hemisphere + volume of the cone

= - n (l)³ + 7- 7t (1)²(1) = n cm³.

3    3

2.    Rachel, an engineering student, was asked to make a model shapecl like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has height of 2 cm, find the oolume of air contained in the model tliat Rachel madę. (Assume the outer and inner dimensions of the model to be nearly the same.)

Sol. Radius of base of cylinder = radius of base of cone

3

= r = — cm.

2

Height of cone (h_x) = 2 cm Height of cylinder (h) = (12 - 4) cm = 8 cm

Yolume of air = 2 x — itr²h + nr²h

-h, + h 3 ^

22    (3f

‘ T * 5 *

<3) ³l^m (

W-2 cm-H w-

— x 2 + 8 3

12 cm

M-2 cm-W -M

^{22    9}    28 aa 3

— x - X — = 66 cm .

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