H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Surface Areas & Volumes, Exercise 4: EXERCISE

A cylindrical tub of radius $5 \mathrm{cm}$ and length $9.8 \mathrm{cm}$ is full of water. A solid in the form of a right circular cone of height $5 \mathrm{cm}$ mounted on a hemisphere of common diameter $5 \mathrm{cm}$ is immersed into the tub, find the volume of water left in the tub.

A solid iron rectangular block of dimension $4.4 \mathrm{m}, 2.6 \mathrm{m}$ and $1 \mathrm{m}$ is cast into a hollow cylindrical pipe of internal radius $30 \mathrm{cm}$ and thickness $5 \mathrm{cm}$. Find the length of the pipe.

A rectangular vessel of dimension $20 \mathrm{cm}\times 16 \mathrm{cm}\times 11 \mathrm{cm}$ is full of water. The water is poured into a conical vessel. The top of the conical vessel has its radius $10 \mathrm{cm}$. If the conical vessel is filled completely, determine its height.

Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions $1.57 \mathrm{m}\times 1.44 \mathrm{m}\times 95 \mathrm{cm}$. The overhead tank has its radius of $60 \mathrm{cm}$ and its height is $95 \mathrm{cm}$. Find the height of the water left in the sump after the overhead tank has been completely filled with water from a sump which had been full. Compare the capacity of the tank with that of the sump. $($Use $\mathrm{\pi }=3.14)$

A cone of height $24 \mathrm{cm}$ and radius of base $6 \mathrm{cm}$ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

A conical vessel whose internal radius is $10 \mathrm{cm}$ and height $36 \mathrm{cm}$ is full of water. The water is emptied into a cylindrical vessel with internal radius $20 \mathrm{cm}$. Find the height to which the water rises.

A conical vessel whose internal radius is $5 \mathrm{cm}$ and height $24 \mathrm{cm}$ is full of water. The water is emptied into a cylindrical vessel with internal radius $10 \mathrm{cm}$. Find the height to which the water rises.

The internal and external diameters of a hollow hemispherical shell are $6 \mathrm{cm}$ and $10 \mathrm{cm}$ respectively. If it is melted and recast into a solid cylinder of diameter $14 \mathrm{cm}$, find the height of the cylinder.