The figure shows the amount of water in two rectangular tanks, N and P, at first. Xavier poured
15 of the water from N into P to fill it to the top, without overflowing.
- How much water was there in Tank N at first?
- Xavier then poured all the water from Tank P into Tank N. 1288 cm3 of water overflowed from Tank N. What was the height of Tank N?
(a)
Volume of water to fill Tank P
= 14 x 10 x 12
= 1680 cm
3
15 of volume of water in Tank N at first = 1680 cm
3
55 of volume of water in Tank N at first = 5 x 1680 = 8400 cm
3 Volume of water in Tank N at first = 8400 cm
3 Volume of water in Tank P at first
= 14 x 10 x 14
= 1960 cm
3 Total volume of water in Tank N and Tank P
= 8400 + 1960
= 10360 cm
3 Final volume of water in Tank N after 1288 cm
3 of water overflowed
= 10360 - 1288
= 9072 cm
3 Base area of Tank N
= 18 x 14
= 252 cm
2 Height of Tank N
= 9072 ÷ 252
= 36 cm
Answer(s): (a) 8400 cm
2 ; (b) 36 cm