The figure shows the amount of water in two rectangular tanks, X and Y, at first. Zane poured
14 of the water from X into Y to fill it to the top, without overflowing.
- How much water was there in Tank X at first?
- Zane then poured all the water from Tank Y into Tank X. 1044 cm3 of water overflowed from Tank X. What was the height of Tank X?
(a)
Volume of water to fill Tank Y
= 18 x 14 x 15
= 3780 cm
3
14 of volume of water in Tank X at first = 3780 cm
3
44 of volume of water in Tank X at first = 4 x 3780 = 15120 cm
3 Volume of water in Tank X at first = 15120 cm
3 Volume of water in Tank Y at first
= 18 x 14 x 18
= 4536 cm
3 Total volume of water in Tank X and Tank Y
= 15120 + 4536
= 19656 cm
3 Final volume of water in Tank X after 1044 cm
3 of water overflowed
= 19656 - 1044
= 18612 cm
3 Base area of Tank X
= 22 x 18
= 396 cm
2 Height of Tank X
= 18612 ÷ 396
= 47 cm
Answer(s): (a) 15120 cm
2 ; (b) 47 cm