The figure shows the amount of water in two rectangular tanks, E and F, at first. Charlie poured
14 of the water from E into F to fill it to the top, without overflowing.
- How much water was there in Tank E at first?
- Charlie then poured all the water from Tank F into Tank E. 2464 cm3 of water overflowed from Tank E. What was the height of Tank E?
(a)
Volume of water to fill Tank F
= 16 x 14 x 14
= 3136 cm
3
14 of volume of water in Tank E at first = 3136 cm
3
44 of volume of water in Tank E at first = 4 x 3136 = 12544 cm
3 Volume of water in Tank E at first = 12544 cm
3 Volume of water in Tank F at first
= 16 x 14 x 18
= 4032 cm
3 Total volume of water in Tank E and Tank F
= 12544 + 4032
= 16576 cm
3 Final volume of water in Tank E after 2464 cm
3 of water overflowed
= 16576 - 2464
= 14112 cm
3 Base area of Tank E
= 18 x 16
= 288 cm
2 Height of Tank E
= 14112 ÷ 288
= 49 cm
Answer(s): (a) 12544 cm
2 ; (b) 49 cm