Mathematics 0580 · IGCSE · Similarity

Similarity — practice question

(a)[2]

Calculate the height of the water in the tank.

(b(i))[3]

Calculate the volume of the tank.

(b(ii))[1]

Write your answer to part (b)(i) in litres.

(c)[3]

Calculate the time taken. Give your answer in hours and minutes.

(d(i))[2]

Using the properties of similar triangles, show that $h = 2(x - 50)$.

(d(ii))[1]

Using $h = 2(x - 50)$, show that the shaded area, in $\text{cm}^2$, is $x^2 - 2500$.

(d(iii))[2]

Find the value of $x$.

(d(iv))[1]

Find the value of $h$.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: $180000\div(\pi 45^2)$

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