Volume of Solid Shapes

Find the total surface area of a cube whose volume is $3375 {\mathrm{cm}}^3$.

Find the volume of a cuboid whose: length $=12 \mathrm{cm}$, breadth $=8 \mathrm{cm}$, height$=10 \mathrm{cm}$

Find the volume of a cuboid whose: length$=8 \mathrm{cm}$, breadth $=3 \mathrm{cm}$, height $=2 \mathrm{cm}$

Which of the two cylinders will have a greater volume? Without doing any calculations, can you suggest whose curved surface area is greater? Check whether the cylinder with the greater volume also has greater surface area.

The edges of a cuboid are in the ratio $1:2:3$ and its surface area is $198 \mathrm{sq}.\mathrm{cm}$. Find the volume of the cuboid.

The curved surface area and the volume of a cylindrical pillar is $550 \mathrm{sq}.\mathrm{cm}$ and $1375{ \mathrm{cm}}^3$. Find its diameter and height.

A rectangular sheet of paper of dimensions $25 \mathrm{cm}\times 22 \mathrm{cm}$ is rolled along its width to form a cylinder. Find the volume of the cylinder so formed.

The circumference of the base of a cylinder is $88 \mathrm{cm}$ and its height is $30 \mathrm{cm}$. Find the volume of the cylinder.

A well is dug $14 \mathrm{m}$ deep. Its radius is $2 \mathrm{m}$. The earth dug out is evenly spread out on a rectangular field of dimensions $10 \mathrm{m}\times 4 \mathrm{m}$. Find the height of the platform raised.

The ratio of the radii of two cylinders of equal heights is $1:3$. Find the ratio of their volumes.

Find the volume of a cylinder whose area of the base is $250 {\mathrm{m}}^2$ and height $2 \mathrm{m}$.

A rectangular tank is $110 \mathrm{cm}$ wide and $70 \mathrm{cm}$ deep. If it can contain $770$ litres of water, what is the length of the tank?

The length of a room is twice its breadth. Its height is $5 \mathrm{m}$. The area of its four walls (including doors and windows) is $210 \mathrm{sq}.\mathrm{m}$. Find its volume.

The outer dimensions of a closed wooden box are $16 \mathrm{cm}$ by $12 \mathrm{cm}$ by $8 \mathrm{cm}$. Thickness of the wood is $1 \mathrm{cm}$. Find the total cost of the wood required to make the box, if $1{ \mathrm{cm}}^3$ of wood costs $₹2.50$.

Two cubes, each of volume $729{ \mathrm{cm}}^3$ are joined end to end. Find the surface area of the resulting cuboid.

How many cubes each of side $4 \mathrm{cm}$ can be cut from a cuboid measuring $16 \mathrm{cm}\times 10 \mathrm{cm}\times 6 \mathrm{cm}$?

Find the capacity of a rectangular cistern in litres whose dimensions are $12 \mathrm{m}\times 3.5 \mathrm{m}\times 5 \mathrm{m}$.

A pit $7 \mathrm{m}$ long and $2.5 \mathrm{m}$ wide is dug to a certain depth. If the volume of the earth taken out of it is $28{ \mathrm{m}}^3$, what is the depth of the pit?

The volume of a cube is $1728 {\mathrm{cm}}^3$. Find its total surface area.

A cardboard box is $1.4 \mathrm{m}$ long, $75 \mathrm{cm}$ wide and $49 \mathrm{cm}$ high. How many bars of soap can be put into it, if each bar measures $6 \mathrm{cm}\times 5 \mathrm{cm}\times 3.5 \mathrm{cm}$?