The figure shows the amount of water in two rectangular tanks, F and G, at first. Luke poured
15 of the water from F into G to fill it to the top, without overflowing.
- How much water was there in Tank F at first?
- Luke then poured all the water from Tank G into Tank F. 1980 cm3 of water overflowed from Tank F. What was the height of Tank F?
(a)
Volume of water to fill Tank G
= 15 x 12 x 14
= 2520 cm
3
15 of volume of water in Tank F at first = 2520 cm
3
55 of volume of water in Tank F at first = 5 x 2520 = 12600 cm
3 Volume of water in Tank F at first = 12600 cm
3 Volume of water in Tank G at first
= 15 x 12 x 16
= 2880 cm
3 Total volume of water in Tank F and Tank G
= 12600 + 2880
= 15480 cm
3 Final volume of water in Tank F after 1980 cm
3 of water overflowed
= 15480 - 1980
= 13500 cm
3 Base area of Tank F
= 20 x 15
= 300 cm
2 Height of Tank F
= 13500 ÷ 300
= 45 cm
Answer(s): (a) 12600 cm
2 ; (b) 45 cm