The figure shows the amount of water in two rectangular tanks, X and Y, at first. Billy 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?
- Billy then poured all the water from Tank Y into Tank X. 20640 cm3 of water overflowed from Tank X. What was the height of Tank X?
(a)
Volume of water to fill Tank Y
= 20 x 18 x 18
= 6480 cm
3
15 of volume of water in Tank X at first = 6480 cm
3
55 of volume of water in Tank X at first = 5 x 6480 = 32400 cm
3 Volume of water in Tank X at first = 32400 cm
3 Volume of water in Tank Y at first
= 20 x 18 x 22
= 7920 cm
3 Total volume of water in Tank X and Tank Y
= 32400 + 7920
= 40320 cm
3 Final volume of water in Tank X after 20640 cm
3 of water overflowed
= 40320 - 20640
= 19680 cm
3 Base area of Tank X
= 24 x 20
= 480 cm
2 Height of Tank X
= 19680 ÷ 480
= 41 cm
Answer(s): (a) 32400 cm
2 ; (b) 41 cm