The figure shows the amount of water in two rectangular tanks, Y and Z, at first. Warren poured
15 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?
- Warren then poured all the water from Tank Z into Tank Y. 16632 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 17
= 4896 cm
3
15 of volume of water in Tank Y at first = 4896 cm
3
55 of volume of water in Tank Y at first = 5 x 4896 = 24480 cm
3 Volume of water in Tank Y at first = 24480 cm
3 Volume of water in Tank Z at first
= 18 x 16 x 19
= 5472 cm
3 Total volume of water in Tank Y and Tank Z
= 24480 + 5472
= 29952 cm
3 Final volume of water in Tank Y after 16632 cm
3 of water overflowed
= 29952 - 16632
= 13320 cm
3 Base area of Tank Y
= 20 x 18
= 360 cm
2 Height of Tank Y
= 13320 ÷ 360
= 37 cm
Answer(s): (a) 24480 cm
2 ; (b) 37 cm