The figure shows the amount of water in two rectangular tanks, T and U, at first. Paul poured
15 of the water from T into U to fill it to the top, without overflowing.
- How much water was there in Tank T at first?
- Paul then poured all the water from Tank U into Tank T. 1428 cm3 of water overflowed from Tank T. What was the height of Tank T?
(a)
Volume of water to fill Tank U
= 14 x 12 x 12
= 2016 cm
3
15 of volume of water in Tank T at first = 2016 cm
3
55 of volume of water in Tank T at first = 5 x 2016 = 10080 cm
3 Volume of water in Tank T at first = 10080 cm
3 Volume of water in Tank U at first
= 14 x 12 x 16
= 2688 cm
3 Total volume of water in Tank T and Tank U
= 10080 + 2688
= 12768 cm
3 Final volume of water in Tank T after 1428 cm
3 of water overflowed
= 12768 - 1428
= 11340 cm
3 Base area of Tank T
= 18 x 14
= 252 cm
2 Height of Tank T
= 11340 ÷ 252
= 45 cm
Answer(s): (a) 10080 cm
2 ; (b) 45 cm