Volume of a Spherical Shell

Q.

The radius of a sphere is $2r,$ then its volume will be

Q. A spherical shell of outer radius $r_2$ and inner radius $r_1$ is made of plastic filled with water. Find the volume available for water.

1. $\frac{4}{3}\pi (r_2^3-r_1^3)$
2. $\frac{4}{3}\pi \left(r_2^3\right)$
3. $\frac{4}{3}\pi \left(r_1^3\right)$
4. $\frac{4}{3}\pi (r_2^3+r_1^3)$

Q. A cube is a cuboid of equal length, width and height.

1. False
2. True

Q.

A pipe is connected to a tank. The water flows out from the tank through the pipe at the rate of $64m^3/min$. Find the time taken by the pipe to empty a volume of $1024m^3$. (in mins)

1. 16

2. 24

3. 32

4. 64

Q. The volume of material required to be extracted from a sphere of radius 4 cm to create a shell of radius 1 cm = cm ${}^3$.

1. 264
2. 288
3. 464
4. 512

Q.

A tank has a capacity of $3584m^3$ that is used by 4 families. If each family uses 4 buckets of water every day, and the volume of the bucket is $16m^3$, then the water in the tank will last for how many weeks?

1. 1 week

2. 2 weeks

3. 4 weeks

4. 3 weeks

Q. If a concentric hemisphere of radius $\frac{R}{2}$ is removed from a radius of hemisphere $R$. Find the ratio of remaining volume to that of removed.

$\left[2\right]$