Number 8
4 marks · HardA swimming pool is 25 m long, 8 m wide, and has an average depth of 2 m. The pool is filled with water at a rate of 40 litres per minute.
Calculate the total volume of the pool in cubic metres (m³).
Work out how many litres of water are needed to fill the pool. (1 m³ = 1000 litres)
Estimate how many hours it will take to fill the pool at the given rate. Show your reasoning.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 400 m³
(b) 400,000 litres
(c) 167 hours (accept answers in range 166–168 hours; accept clear working) hours · must show Clear reasoning shown, Final answer in hours
Common mistakes: Not converting m³ to litres; Incorrect division of total litres by rate per minute
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Calculates volume: 25 × 8 × 2 = 400 m³
A1 (b) · 1 mark · Converts 400 m³ to 400,000 litres (1 m³ = 1000 litres) (follow-through)
M2 (c) · 1 mark · Divides total litres by 40 to find minutes to fill; shows method. (follow-through)
A2 (c) · 1 mark · Converts minutes to hours and gives answer appropriately rounded; marks reasoning as well as final answer. (follow-through)
Worked solution
a) Volume = length × width × depth:
b) 1 m³ = 1000 litres, so:
c) Time to fill the pool = total litres ÷ rate (litres/min):
Convert minutes to hours:
So, it will take about 167 hours to fill the pool.