The figure shows the amount of water in two rectangular tanks, D and E, at first. Sean poured
15 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?
- Sean then poured all the water from Tank E into Tank D. 10140 cm3 of water overflowed from Tank D. What was the height of Tank D?
(a)
Volume of water to fill Tank E
= 20 x 17 x 16
= 5440 cm
3
15 of volume of water in Tank D at first = 5440 cm
3
55 of volume of water in Tank D at first = 5 x 5440 = 27200 cm
3 Volume of water in Tank D at first = 27200 cm
3 Volume of water in Tank E at first
= 20 x 17 x 19
= 6460 cm
3 Total volume of water in Tank D and Tank E
= 27200 + 6460
= 33660 cm
3 Final volume of water in Tank D after 10140 cm
3 of water overflowed
= 33660 - 10140
= 23520 cm
3 Base area of Tank D
= 24 x 20
= 480 cm
2 Height of Tank D
= 23520 ÷ 480
= 49 cm
Answer(s): (a) 27200 cm
2 ; (b) 49 cm