Volume of Solids

Find the volume of the object with given cross-section.

Find the volumes of the figure given below.

The guttering pictured here has a semicircular cross-section. Find the volume of water that the guttering will hold when full.

Water is discharged from a pipe of cross-section area $6 {\mathrm{cm}}^2$ at the speed of $10 \mathrm{m}/\mathrm{s}$. Calculate the volume of water discharged in $\mathrm{litres} \mathrm{per} \mathrm{minute}$.

Water is discharged from a pipe of cross-section area $6 {\mathrm{cm}}^2$ at the speed of $10 \mathrm{m}/\mathrm{s}$. Calculate the volume of water discharged in ${\mathrm{cm}}^3 \mathrm{per} \sec$.

The dimensions of a Class Room are $100 \mathrm{m}, 60 \mathrm{m}$ and $20 \mathrm{m}$. How many students can sit in the room, if each requires $120 {\mathrm{m}}^3$$?$

The internal length, breadth and height of a box are $45 \mathrm{cm}, 90 \mathrm{cm}$ and $27 \mathrm{cm}$. Find the largest number of cubes which can be placed inside this box if the edge of each cube is $9 \mathrm{cm}$.

The internal length, breadth and height of a box are $40 \mathrm{cm}, 30 \mathrm{cm}$ and $20 \mathrm{cm}$. Find the largest number of cubes which can be placed inside this box if the edge of each cube is $2 \mathrm{cm}$.

The internal length, breadth and height of a box are $40 \mathrm{cm}, 30 \mathrm{cm}$ and $20 \mathrm{cm}$. Find the largest number of cubes which can be placed inside this box if the edge of each cube is $5 \mathrm{cm}$.

The edge of a cube is $15 \mathrm{cm},$ then its volume will be $3375 {\mathrm{cm}}^3$.

A cube of $2 \mathrm{m}$ long side is cut off from a cube of $3 \mathrm{m}$ long side. Remaining volume of the cube will be $5 {\mathrm{m}}^3$.

The edge and diagonal of a cube are in the ratio $1 : 3$.

Total number of diagonals in a cube or cuboid is $4$.

If a rectangular tank has length $15 \mathrm{m}$, breadth $10 \mathrm{m}$ and height $8 \mathrm{m}$. How much kilolitre of water can be stored in it$?$

Total surface area of a rectangular body is $8400 {\mathrm{cm}}^2$. If length and breadth of the body is$40 \mathrm{cm}$ and $30 \mathrm{cm}$ respectively, find its height in $\mathrm{cm}$.

Water is discharged from a pipe of cross-section area $4.2 {\mathrm{cm}}^2$ at the speed of $15 \mathrm{m}/\mathrm{s}$. Calculate the volume of water discharged in ${\mathrm{cm}}^3 \mathrm{per} \sec$.

The figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetres. Assume all angle right angles.

The dimensions of a Class Room are $200 \mathrm{m}, 120 \mathrm{m}$ and $30 \mathrm{m}$. How many students can sit in the room, if each requires $150 {\mathrm{m}}^3$ of air$?$

A $4 \mathrm{cm}$ cube is cut into $1 \mathrm{cm}$ cubes. Calculate the total surface area in ${\mathrm{cm}}^2$of all the small cubes.

A solid cube of side $12 \mathrm{c}\mathrm{m}$ is cut into eight cubes of equal volume. The ratio between their surface areas is