The figure shows the amount of water in two rectangular tanks, X and Y, at first. Michael 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?
- Michael then poured all the water from Tank Y into Tank X. 2192 cm3 of water overflowed from Tank X. What was the height of Tank X?
(a)
Volume of water to fill Tank Y
= 16 x 13 x 13
= 2704 cm
3
14 of volume of water in Tank X at first = 2704 cm
3
44 of volume of water in Tank X at first = 4 x 2704 = 10816 cm
3 Volume of water in Tank X at first = 10816 cm
3 Volume of water in Tank Y at first
= 16 x 13 x 17
= 3536 cm
3 Total volume of water in Tank X and Tank Y
= 10816 + 3536
= 14352 cm
3 Final volume of water in Tank X after 2192 cm
3 of water overflowed
= 14352 - 2192
= 12160 cm
3 Base area of Tank X
= 20 x 16
= 320 cm
2 Height of Tank X
= 12160 ÷ 320
= 38 cm
Answer(s): (a) 10816 cm
2 ; (b) 38 cm