The figure shows the amount of water in two rectangular tanks, J and K, at first. Riordan poured
15 of the water from J into K to fill it to the top, without overflowing.
- How much water was there in Tank J at first?
- Riordan then poured all the water from Tank K into Tank J. 8968 cm3 of water overflowed from Tank J. What was the height of Tank J?
(a)
Volume of water to fill Tank K
= 19 x 16 x 15
= 4560 cm
3
15 of volume of water in Tank J at first = 4560 cm
3
55 of volume of water in Tank J at first = 5 x 4560 = 22800 cm
3 Volume of water in Tank J at first = 22800 cm
3 Volume of water in Tank K at first
= 19 x 16 x 19
= 5776 cm
3 Total volume of water in Tank J and Tank K
= 22800 + 5776
= 28576 cm
3 Final volume of water in Tank J after 8968 cm
3 of water overflowed
= 28576 - 8968
= 19608 cm
3 Base area of Tank J
= 24 x 19
= 456 cm
2 Height of Tank J
= 19608 ÷ 456
= 43 cm
Answer(s): (a) 22800 cm
2 ; (b) 43 cm