The figure shows the amount of water in two rectangular tanks, Q and R, at first. Tim poured
14 of the water from Q into R to fill it to the top, without overflowing.
- How much water was there in Tank Q at first?
- Tim then poured all the water from Tank R into Tank Q. 3360 cm3 of water overflowed from Tank Q. What was the height of Tank Q?
(a)
Volume of water to fill Tank R
= 16 x 14 x 15
= 3360 cm
3
14 of volume of water in Tank Q at first = 3360 cm
3
44 of volume of water in Tank Q at first = 4 x 3360 = 13440 cm
3 Volume of water in Tank Q at first = 13440 cm
3 Volume of water in Tank R at first
= 16 x 14 x 18
= 4032 cm
3 Total volume of water in Tank Q and Tank R
= 13440 + 4032
= 17472 cm
3 Final volume of water in Tank Q after 3360 cm
3 of water overflowed
= 17472 - 3360
= 14112 cm
3 Base area of Tank Q
= 18 x 16
= 288 cm
2 Height of Tank Q
= 14112 ÷ 288
= 49 cm
Answer(s): (a) 13440 cm
2 ; (b) 49 cm