The figure shows the amount of water in two rectangular tanks, X and Y, at first. Pierre poured
15 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?
- Pierre then poured all the water from Tank Y into Tank X. 8460 cm3 of water overflowed from Tank X. What was the height of Tank X?
(a)
Volume of water to fill Tank Y
= 18 x 16 x 15
= 4320 cm
3
15 of volume of water in Tank X at first = 4320 cm
3
55 of volume of water in Tank X at first = 5 x 4320 = 21600 cm
3 Volume of water in Tank X at first = 21600 cm
3 Volume of water in Tank Y at first
= 18 x 16 x 19
= 5472 cm
3 Total volume of water in Tank X and Tank Y
= 21600 + 5472
= 27072 cm
3 Final volume of water in Tank X after 8460 cm
3 of water overflowed
= 27072 - 8460
= 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) 21600 cm
2 ; (b) 47 cm