The figure shows the amount of water in two rectangular tanks, J and K, at first. Ethan 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?
- Ethan then poured all the water from Tank K into Tank J. 2400 cm3 of water overflowed from Tank J. What was the height of Tank J?
(a)
Volume of water to fill Tank K
= 16 x 12 x 13
= 2496 cm
3
15 of volume of water in Tank J at first = 2496 cm
3
55 of volume of water in Tank J at first = 5 x 2496 = 12480 cm
3 Volume of water in Tank J at first = 12480 cm
3 Volume of water in Tank K at first
= 16 x 12 x 15
= 2880 cm
3 Total volume of water in Tank J and Tank K
= 12480 + 2880
= 15360 cm
3 Final volume of water in Tank J after 2400 cm
3 of water overflowed
= 15360 - 2400
= 12960 cm
3 Base area of Tank J
= 18 x 16
= 288 cm
2 Height of Tank J
= 12960 ÷ 288
= 45 cm
Answer(s): (a) 12480 cm
2 ; (b) 45 cm