The figure shows the amount of water in two rectangular tanks, Y and Z, at first. Ben poured
13 of the water from Y into Z to fill it to the top, without overflowing.
- How much water was there in Tank Y at first?
- Ben then poured all the water from Tank Z into Tank Y. 3888 cm3 of water overflowed from Tank Y. What was the height of Tank Y?
(a)
Volume of water to fill Tank Z
= 18 x 16 x 15
= 4320 cm
3
13 of volume of water in Tank Y at first = 4320 cm
3
33 of volume of water in Tank Y at first = 3 x 4320 = 12960 cm
3 Volume of water in Tank Y at first = 12960 cm
3 Volume of water in Tank Z at first
= 18 x 16 x 18
= 5184 cm
3 Total volume of water in Tank Y and Tank Z
= 12960 + 5184
= 18144 cm
3 Final volume of water in Tank Y after 3888 cm
3 of water overflowed
= 18144 - 3888
= 14256 cm
3 Base area of Tank Y
= 22 x 18
= 396 cm
2 Height of Tank Y
= 14256 ÷ 396
= 36 cm
Answer(s): (a) 12960 cm
2 ; (b) 36 cm