A shuttle cock used for playing badminton has the shape of the combination of

**A. ** a cylinder and a sphere

**B. ** a hemisphere and a cone

**C. ** a sphere and a cone

**D. ** frustum of a cone and a hemisphere

**Answer : ****Option D**

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A spherical ball of radius *r*_{1}
units is melted to make 8 new identical balls each of radius *r*_{2}
units. Then *r*_{1} : *r*_{2} is

**A. ** 2:1

**B. ** 1:2

**C. ** 4:1

**D. ** 1:4

**Answer : ****Option A**

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The volume (in cm^{3})
of the greatest sphere that can be cut off from a cylindrical log of wood of
base radius 1 cm and height 5 cm is

**A. ** 4/3 *π*

**B. ** 10/3 *π*

**C. ** 5 *π*

**D. ** 20/3 *π*

**Answer : ****Option A**

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The height and radius of
the cone of which the frustum is a part are *h*_{1} units and *r*_{1}
units respectively. Height of the frustum is *h*_{2} units and
radius of the smaller base is *r*_{2}* *units. If* h*_{2}*
*:* h*_{1}* *=* *1 : 2* *then* r*_{2}*
*:* r*_{1}* *is

**A. ** 1 : 3

**B. ** 1 : 2

**C. ** 2 : 1

**D. ** 3 : 1

**Answer : ****Option B**

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The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

**A. ** 1:2:3

**B. ** 2:1:3

**C. ** 1:3:2

**D. ** 3:1:2

**Answer : ****Option D**

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