Measurement, STD2 2026 HSC 33

A rectangular tub has length 50 cm, width 20 cm and unknown height \((h)\).

Ten identical cylinders are arranged inside the tub in two rows of five.

Each cylinder has diameter 10 cm and height \(h\) cm.

Exactly 3 litres of water is poured into the tub to fill all the spaces around the cylinders.

What is the height of the tub, correct to the nearest whole number? (4 marks)

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\(14\ \text{cm}\)

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\(\text{Water volume}=3\times1000=3000\ \text{cm}^3\)

\(\text{Tub width = 20 cm = 2 × cylinder diameter}\)

\(\text{Cylinder radius}\ = \dfrac{20}{4}=5\ \text{cm}\)

\(\text{Tub volume (method 1)}\ = 50 \times 20 \times h = 1000h\)

\(\text{Using cylinder volume}\ = \pi \times r^{2} \times h:\)

\(\text{Tub volume (method 2)}\ = (10 \times \pi \times 5^{2} \times h) +3000 = 250\pi h +3000\)

\(\text{Equating volumes:}\)

\(\therefore\ \text{Height of tub = 14 cm (nearest whole)}\)