Volume of Sphere and Hemisphere

Q.

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 7 cm in it. The increase in the height of water in the container is :

1. 10.1 cm
2. 9.33 cm
3. 4.5 cm
4. 28 cm

Q.

A spherical glass vessel has a cylindrical neck $8cm$ long, $2cm$ in diameter; the diameter of the spherical part is $8.5cm.$. By measuring the amount of water it holds, a child finds its volume to be $345c{m}^3$. Check whether she is correct, taking the above as the inside measurements, and $\mathrm{\pi }=3.14$.

Q. If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

1. $2:\sqrt[3]{32}$
2. $1:\sqrt[3]{37}$
3. $1:\sqrt[3]{32}$
4. $1:\sqrt[3]{33}$

Q.

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

1. 144 cm³

2. 169 cm³

3. 132 cm³

4. 154 cm³

Q. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. The number of lead shots dropped in the vessel is :

1. 50
2. 25
3. 100
4. 150

Q. An iron spherical ball of radius 21 cm is melted and is re-cast into hemispheres of radius 7 cm. The number of hemispheres formed will be :

1. 27
2. 64
3. 54
4. 16

Q. Outer surface area of a hollow iron sphere is 1256 cm${}^2$. If thickness of iron is 1 cm, its capacity = .

1. 3052.08 $c{m}^3$
2. 3051.08 $c{m}^3$
3. 3053.08 $c{m}^3$

Q.

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.

1. $8$ units

2. $2\sqrt{2}$ units

3. $24$ units

4. $64$ units

Q. The ratio of volume and total surface area of a solid sphere is 8 : 1, then value of radius = cm.

1. 2
2. 24
3. 64

Q.

A measuring jar with an internal diameter of $10cm$ is partially filled with water. Four equal spherical balls of a diameter of $2cm$ each are dropped in it and they sink down in the water completely. What will be the change in the level of water in the jar?