WAEC 2010 · Paper 2 · Q5

(a)
The diagonals of a rhombus are $14\text{ cm}$ and $9\text{ cm}$ . Calculate, correct to the nearest centimetre, the perimeter of the rhombus.
(b)
The cross section of a rectangular tank measures $1.2\text{ m}$ by $0.9\text{ m}$ . It contains water to a depth of $0.4\text{ m}$ . If a cubical block of side $50\text{ cm}$ is lowered into the tank, calculate, correct to 2 significant figures, the rise in the water level (in metres).

Worked solution (try it first)

(a)

The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right-angled triangle with legs $7\text{ cm}$ and $4.5\text{ cm}$ .
Side $= \sqrt{7^2 + 4.5^2}$
$= \sqrt{69.25}$
$= 8.32\text{ cm}$ .
All four sides are equal: perimeter $= 4 \times 8.32 = 33.3$ , which is $33\text{ cm}$ to the nearest centimetre.

(b)

Work in metres: the block is $0.5\text{ m}$ on a side, so its volume is $0.5^3 = 0.125\text{ m}^3$ .
The block sinks below the surface (the water will not be $0.5\text{ m}$ deep), so it pushes up $0.125\text{ m}^3$ of water over the base area $1.2 \times 0.9 = 1.08\text{ m}^2$ .
Rise $= \dfrac{0.125}{1.08} = 0.1157\text{ m}$ .
The water level rises by $0.12\text{ m}$ to 2 significant figures.

Report a problem with this question