Area & Volume of Similar Shapes Practice Questions

Work out the value of $x$.

The area of sign A is $32\text{ cm}^2$.

Work out the area of sign B.

The total surface area of candle A is $240\text{ cm}^2$.

Work out the total surface area of candle B.

The volume of candle B is $810\text{ cm}^3$.

Work out the volume of candle A.

P and Q are two mathematically similar solid glass paperweights.

surface area of P : surface area of Q $= 5 : 8$

The volume of P is $90\text{ cm}^3$.

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

....................................................... cm$^3$

The curved surface area of the original cone is $900\text{ cm}^2$.

Work out the curved surface area of the small cone that is removed.

The volume of the original cone is $1250\text{ cm}^3$.

Work out the volume of the solid that is left after the small cone has been removed.

Work out the height of the large tin.
You must show all your working.

The label on the small tin has an area of $120\text{ cm}^2$.

The label on the large tin is mathematically similar to the label on the small tin.

Work out the area of the label on the large tin.

Three solid containers A, B and C are mathematically similar.

the height of A : the height of B $= 2 : 3$

the volume of B : the volume of C $= 27 : 125$

The surface area of container A is $52\text{ cm}^2$.

Work out the surface area of container C.
You must show all your working.

....................................................... cm$^2$

Water is poured into the empty glass to a depth of $9$ cm.

Show that the glass then contains $21.6\%$ of the amount of water it holds when full.

The glass holds $250$ ml of water when full.

Water is poured into the empty glass until the glass contains $100$ ml of water.

Work out the depth of the water in the glass.
Give your answer correct to 1 decimal place.

....................................................... cm