Volume of a sphere

Q.

The volumes of the two spheres are in the ratio $64:27.$ Find the ratio of their surface areas.

Q.

Find the volumes of a sphere whose surface area is $154c{m}^2$.

Q.

The volume of a sphere of radius 21 cm is

1. 30008 cm³

2. 38808 cm³

3. 38000 cm³

4. 38880 cm³

Q.

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is

1. $\pi :3$
   

2. $\pi :4$
   

3. $\pi :6$
   

4. $\pi :2$
   

Q. Question 10
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is:

A) 1:4
B) 1:3
C) 2:3
D) 2:1

Q.

If the ratio of volumes of two spheres is 1 : 8 then the ratio of their surface areas is

1. 1 : 2

2. 1 : 8

3. 1 : 16

4. 1 : 4

Q.

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Q.

The surface areas of two spheres are in the ratio 1 : 4. Find the ratio of their volumes.

Q. Question 5
Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the sphere, if the diameter of the smaller one is 5 cm.

Q.

The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be

1. $12\pi c{m}^3$
   

2. $27\pi c{m}^3$
   

3. $108\pi c{m}^3$
   

4. $36\pi c{m}^3$

Q.

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

Q. A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm.Their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm.If the cone is then removed, find the height to which water level will fall.

Q. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is:

1. 12 m
2. 18 m
3. 36 m
4. 66 m

Q.

The difference between the radii of 3^rd and 4^th orbits of ${\mathrm{Li}}^{2+}$ is ${\mathrm{\Delta R}}_1.$ The difference between the radii of 3^rd and 4^th orbits of ${\mathrm{He}}^{+}$ is ΔR₂. Ratio ${\mathrm{\Delta R}}_1:{\mathrm{\Delta R}}_2$is:

1. 8:3

2. 3:8

3. 3:2

4. 2:3

Q. A sphere and a cube have same surface area. Show that the ratio of the volume of sphere to that of cube is √6:√π.

Q. Question 9
A shopkeeper has one spherical laddu of radius 5 cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?

Q.

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm, Find the volume of metal contained in the shell. Also find its outer surface area.

Q. The volume of the.two ratio is 125:64find the ratio of their radii

Q.

The height of a cone is 4 cm and its base radius is 3 cm. The total surface area of the cone is:

1. 68 $c{m}^2$

2. 75.42 $c{m}^2$

3. 89.5 $c{m}^2$

4. 93.23 $c{m}^2$

Q.

The volume of a spherical balloon is increasing at the rate of $40$ $\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$min$}\right.$.

The rate of change of the surface area of the balloon at the instant when its radius is $8$ $cm$, is

1. $\frac{5}{2}\frac{sq.cm}{min}$

2. $5\frac{sq.cm}{min}$

3. $10\frac{sq.cm}{min}$

4. $20\frac{sq.cm}{min}$

Q.

Find the volume of the composite solid. Round your answer to the nearest tenth.

Q.

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is

1. 2 : 1

2. 1 : 1

3. 2 : 3

4. 1 : 2

Q.

The volume of a sphere is 38808 $c{m}^3$. Find its radius and hence its surface area.

Q.

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

Q.

The radii of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height $2\frac{2}{3}$ cm. Find the diameter of the cylinder.

Q. If a sphere, a cone and a cylinder have the same heights and same radii, then the ratio of their volumes is equal to

1. 4 : 2 : 5
2. 2 : 1 : 4
3. 3 : 2 : 4
4. 2 : 1 : 3

Q.

If a sphere is inscribed in a cube, find the ratio of the volume of the cube to the volume of the sphere.

Q. Question 6
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $c{m}^3$ of iron has approximately 8 g mass.

Q.

A hollow spherical shell is made of a metal of density 4.5 g per $c{m}^3$.If its internal and external radii are 8 cm and 9 cm respectively, find the weight of the shell.

Q.

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls off equal radius, then the surface area of each ball (in sq. cm) is

1. $75\pi$
   

2. $60\pi$
   

3. $100\pi$
   

4. $50\pi$