The figure shows the amount of water in two rectangular tanks, P and Q, at first. Cole poured
13 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?
- Cole then poured all the water from Tank Q into Tank P. 3360 cm3 of water overflowed from Tank P. What was the height of Tank P?
(a)
Volume of water to fill Tank Q
= 16 x 14 x 14
= 3136 cm
3
13 of volume of water in Tank P at first = 3136 cm
3
33 of volume of water in Tank P at first = 3 x 3136 = 9408 cm
3 Volume of water in Tank P at first = 9408 cm
3 Volume of water in Tank Q at first
= 16 x 14 x 18
= 4032 cm
3 Total volume of water in Tank P and Tank Q
= 9408 + 4032
= 13440 cm
3 Final volume of water in Tank P after 3360 cm
3 of water overflowed
= 13440 - 3360
= 10080 cm
3 Base area of Tank P
= 18 x 16
= 288 cm
2 Height of Tank P
= 10080 ÷ 288
= 35 cm
Answer(s): (a) 9408 cm
2 ; (b) 35 cm