The figure shows the amount of water in two rectangular tanks, M and N, at first. Riordan poured
15 of the water from M into N to fill it to the top, without overflowing.
- How much water was there in Tank M at first?
- Riordan then poured all the water from Tank N into Tank M. 2400 cm3 of water overflowed from Tank M. What was the height of Tank M?
(a)
Volume of water to fill Tank N
= 16 x 13 x 11
= 2288 cm
3
15 of volume of water in Tank M at first = 2288 cm
3
55 of volume of water in Tank M at first = 5 x 2288 = 11440 cm
3 Volume of water in Tank M at first = 11440 cm
3 Volume of water in Tank N at first
= 16 x 13 x 15
= 3120 cm
3 Total volume of water in Tank M and Tank N
= 11440 + 3120
= 14560 cm
3 Final volume of water in Tank M after 2400 cm
3 of water overflowed
= 14560 - 2400
= 12160 cm
3 Base area of Tank M
= 20 x 16
= 320 cm
2 Height of Tank M
= 12160 ÷ 320
= 38 cm
Answer(s): (a) 11440 cm
2 ; (b) 38 cm