The figure shows the amount of water in two rectangular tanks, P and Q, at first. Neave poured
14 of the water from P into Q to fill it to the top, without overflowing.
- How much water was there in Tank P at first?
- Neave then poured all the water from Tank Q into Tank P. 9480 cm3 of water overflowed from Tank P. What was the height of Tank P?
(a)
Volume of water to fill Tank Q
= 20 x 18 x 17
= 6120 cm
3
14 of volume of water in Tank P at first = 6120 cm
3
44 of volume of water in Tank P at first = 4 x 6120 = 24480 cm
3 Volume of water in Tank P at first = 24480 cm
3 Volume of water in Tank Q at first
= 20 x 18 x 21
= 7560 cm
3 Total volume of water in Tank P and Tank Q
= 24480 + 7560
= 32040 cm
3 Final volume of water in Tank P after 9480 cm
3 of water overflowed
= 32040 - 9480
= 22560 cm
3 Base area of Tank P
= 24 x 20
= 480 cm
2 Height of Tank P
= 22560 ÷ 480
= 47 cm
Answer(s): (a) 24480 cm
2 ; (b) 47 cm