The figure shows the amount of water in two rectangular tanks, D and E, at first. Jenson poured
13 of the water from D into E to fill it to the top, without overflowing.
- How much water was there in Tank D at first?
- Jenson then poured all the water from Tank E into Tank D. 2624 cm3 of water overflowed from Tank D. What was the height of Tank D?
(a)
Volume of water to fill Tank E
= 16 x 14 x 14
= 3136 cm
3
13 of volume of water in Tank D at first = 3136 cm
3
33 of volume of water in Tank D at first = 3 x 3136 = 9408 cm
3 Volume of water in Tank D at first = 9408 cm
3 Volume of water in Tank E at first
= 16 x 14 x 16
= 3584 cm
3 Total volume of water in Tank D and Tank E
= 9408 + 3584
= 12992 cm
3 Final volume of water in Tank D after 2624 cm
3 of water overflowed
= 12992 - 2624
= 10368 cm
3 Base area of Tank D
= 18 x 16
= 288 cm
2 Height of Tank D
= 10368 ÷ 288
= 36 cm
Answer(s): (a) 9408 cm
2 ; (b) 36 cm