Volume & Surface Area Practice Questions

Work out the volume of the trough. Give your answer in $\text{cm}^3$.

Write down the capacity of the trough in litres.

Work out the volume of the candle. Give your answer correct to 3 significant figures.

The wax used to make the candle has a density of $0.9\ \text{g/cm}^3$.

Work out the mass of the candle. Give your answer correct to 3 significant figures.

Work out the volume of the prism.

Work out the total surface area of the prism.

Work out the vertical height of the pyramid.

The pyramid is cut from a solid cube of glass of side $9$ cm.

Work out the percentage of the cube's volume that is wasted. Give your answer correct to 3 significant figures.

A water tank is in the shape of a cylinder with radius $40$ cm. The tank is empty.

Water flows into the tank at a rate of $15$ litres per minute.

Work out how long it takes for the depth of water in the tank to reach $75$ cm. Give your answer in minutes, correct to 3 significant figures.

Show that the slant height of the cone is $12.5$ cm.

Work out the total surface area of the toy. Give your answer correct to 3 significant figures.

Work out the total volume of the silo. Give your answer in $\text{m}^3$ correct to 3 significant figures.

The silo is filled completely with grain. The density of the grain is $750\ \text{kg/m}^3$.

Work out the mass of the grain in the silo. Give your answer correct to 3 significant figures.

A tank is in the shape of a cuboid. The base of the tank is a rectangle measuring $45$ cm by $30$ cm and the tank is $30$ cm deep.

The tank contains water to a depth of $20$ cm.

A solid metal sphere of radius $7$ cm is placed in the tank so that it is completely covered by the water. No water is lost from the tank.

Work out the new depth of the water. Give your answer correct to 3 significant figures.

Volume of sphere $=\frac{4}{3}\pi r^3$

A bucket is in the shape of a frustum of a cone, formed by removing a small cone from a larger cone.

The circular top of the bucket has radius $15$ cm, the circular base has radius $9$ cm and the depth of the bucket is $24$ cm.

Volume of cone $=\frac{1}{3}\pi r^2 h$

The bucket is filled completely with water.

Work out the volume of water in the bucket. Give your answer in litres correct to 3 significant figures.

A solid metal sphere has radius $6$ cm.

The sphere is melted down. $5\%$ of the metal is lost in the melting process.

All of the remaining metal is used to make solid cones. Each cone has base radius $2$ cm and vertical height $4.5$ cm.

Work out the greatest number of complete cones that can be made.

Volume of sphere $=\frac{4}{3}\pi r^3$

Volume of cone $=\frac{1}{3}\pi r^2 h$

A solid cylinder has a height equal to its diameter.

The total surface area of the cylinder is $150\pi\ \text{cm}^2$.

Work out the volume of the cylinder. Give your answer correct to 3 significant figures.

You must show all your working.