R. S. Aggarwal Solutions for Chapter: Volume and Surface Area, Exercise 2: EXERCISE 24B

The internal diameter of a cylindrical pipe is $5 \mathrm{mm}$. Water passes through it at $10 \mathrm{m}$ per minute and falls into a conical vessel of diameter $40 \mathrm{cm}$ and depth $21 \mathrm{cm}$. How much time will be taken to fill this vessel?

A metallic cube of edge $2.5 \mathrm{cm}$ is melted and moulded into a cuboid of length$1.25 \mathrm{cm}$ and breadth $0.25 \mathrm{cm}$. Find the difference between the total surface areas of the resulting cuboid and the given cube.

The volume of a right circular cone is the same as that of a right circular cylinder. This cylinder is $9 \mathrm{cm}$ high and the diameter of its base is $60 \mathrm{cm}$ while the height of the cone is $108 \mathrm{cm}$. Find the diameter of the base of the cone.

From a hemisphere of radius $\mathrm{r} \mathrm{cm}$, a sphere of maximum volume has been cut. Find the ratio of the volume of hemisphere and that of the sphere.

A $45 \mathrm{cm}$ high bucket is in the form of frustum of a cone. The radii of its faces are $28 \mathrm{cm}$ and $7 \mathrm{cm}$. Find the capacity of the bucket..

A $45 \mathrm{cm}$ high bucket is in the form of frustum of a cone. The radii of its faces are $28 \mathrm{cm}$ and $7 \mathrm{cm}$. Find the total surface area of the bucket.

Find the length of the longest pole that can be put in a room $10 \mathrm{m}\times 8 \mathrm{m}\times 5 \mathrm{m}$.

A river $2 \mathrm{m}$ deep and $45 \mathrm{m}$ wide is flowing at the rate of $3 \mathrm{km}$ per hour. Find how much water runs into the sea per minute.