The radio of base of a one 5 cm and to height 12 cm. The slant height of the cone ___________

(a)

12 cm

(b)

17 cm

(c)

7 cm

(d)

60 cm

If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

(a)

3:1:2

(b)

3:2:1

(c)

1:2:3

(d)

1:3:2

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

(a)

64

(b)

216

(c)

512

(d)

16

The volume of a frustum if a cone of height L and ends-radio and r₁ and r₂ is ___________

(a)

\(\frac{1}{3}\)πh1(r₁²+r₂²+r₁r₂)

(b)

\(\frac{1}{3}\)πh(r₁²+r₂²-r₁r₂)

(c)

πh(r₁²+r₂²+r₁r₂)

(d)

πh(r₁²+r₂²-r₁r₂)

It S₁ denotes the total surface area of a sphere of radius r and S₂ denotes the total surface area of a cylinder of base radius r and height 2r, then ___________

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

The ratio of the volumes of two spheres is 8 : 27. If r and R are the radii of sphere respectively, Then (R - r) : r is ___________

(a)

1:2

(b)

1:3

(c)

2:3

(d)

4:9

The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

(a)

3 times

(b)

6 times

(c)

9 times

(d)

27 times

The height of a cone is 60 cm. A small cone is cut off at the top by plane parallel to the base and its volume is \(\left[ \frac { 1 }{ 64 } \right] ^{ th }\) the volume of the original cone. Then the height of the smaller cone is ___________

(a)

45 cm

(b)

30 cm

(c)

15 cm

(d)

20 cm

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is ___________

(a)

15 cm

(b)

12 cm

(c)

10 cm

(d)

17 cm

A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is ___________

(a)

1:3

(b)

\(1:\sqrt { 3 } \)

(c)

1:1

(d)

\(\sqrt { 3 } :1\)

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

(a)

10 cm

(b)

15 cm

(c)

18 cm

(d)

24 cm

The curved surface area of a cylinder is 264 cm² and its volume is 924 cm². The ratio of diameter to its height is ___________

(a)

3:7

(b)

7:3

(c)

6:7

(d)

7:6

When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as \(\frac { 1 }{ 3 } \). What is the radius of the sphere?

(a)

24 cm

(b)

9cm

(c)

54cm

(d)

4.5cm

A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 1 }{ 4 } \)

(c)

\(\frac { 1 }{ 2 } \)

(d)

\(\frac { 1 }{ 8 } \)