Mathematics 0580 · IGCSE · Surface area and volume

Surface area and volume — practice question

The sketch is of a cylindrical flower vase with radius $r$ and height $h$. Its volume $V$ is given by $V = \pi r^2 h$. Its surface area $A$ is given by $A = 2\pi r h + \pi r^2$. The sketch is not drawn to scale.
(a(i))[3]

Calculate the volume of the vase. State the units for your answer.

(a(ii))[2]

Calculate the vase’s surface area.

(b)[2]

Make $h$ the subject of $A = 2\pi r h + \pi r^2$.

(c)[2]

Factorise $2\pi r h + \pi r^2$ completely.

(d(i))[2]

For this vase and the vase in part (a), the radius ratio is $4 : 6$ and the height ratio is $15 : 22.5$. Write these ratios in simplest form.

(d(ii))[1]

State the mathematical word needed to finish the statement. The ratios show that the two vases are ____________________.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $754$–$754.1\text{ cm}^3$

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