The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer, correct to the nearest km.

Radius of wheel = $\dfrac{\text{Diameter of wheel}}{2} = \dfrac{84}{2}$ = 42 cm.

Distance covered by wheel in 1 revolution = Circumference of wheel = 2πr

= $2 \times \dfrac{22}{7} \times 42$

= 264 cm.

Distance covered by wheel in 5 revolutions = 5 × 264 = 1320 cm.

∴ Wheel covers 1320 cm in 1 second.

$\text{Speed } = \dfrac{\text{Distance}}{\text{Time}} \\[1em] = \dfrac{1320 \times 10^{-5} \text{ km}}{\dfrac{1}{60 \times 60} \text{ hr}} \\[1em] = 1320 \times 60 \times 60 \times 10^{-5} \\[1em] = 4752000 \times 10^{-5} \\[1em] = 47.52 ≈ 48\text{ km/hr}.$

Hence, speed of wheel = 48 km/hr.