The figure shows the amount of water in two rectangular tanks, X and Y, at first. Michael poured
13 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?
- Michael then poured all the water from Tank Y into Tank X. 1584 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 16
= 4608 cm
3
13 of volume of water in Tank X at first = 4608 cm
3
33 of volume of water in Tank X at first = 3 x 4608 = 13824 cm
3 Volume of water in Tank X at first = 13824 cm
3 Volume of water in Tank Y at first
= 18 x 16 x 20
= 5760 cm
3 Total volume of water in Tank X and Tank Y
= 13824 + 5760
= 19584 cm
3 Final volume of water in Tank X after 1584 cm
3 of water overflowed
= 19584 - 1584
= 18000 cm
3 Base area of Tank X
= 20 x 18
= 360 cm
2 Height of Tank X
= 18000 ÷ 360
= 50 cm
Answer(s): (a) 13824 cm
2 ; (b) 50 cm