The figure shows the amount of water in two rectangular tanks, R and S, at first. Jenson poured
13 of the water from R into S to fill it to the top, without overflowing.
- How much water was there in Tank R at first?
- Jenson then poured all the water from Tank S into Tank R. 4104 cm3 of water overflowed from Tank R. What was the height of Tank R?
(a)
Volume of water to fill Tank S
= 19 x 16 x 16
= 4864 cm
3
13 of volume of water in Tank R at first = 4864 cm
3
33 of volume of water in Tank R at first = 3 x 4864 = 14592 cm
3 Volume of water in Tank R at first = 14592 cm
3 Volume of water in Tank S at first
= 19 x 16 x 18
= 5472 cm
3 Total volume of water in Tank R and Tank S
= 14592 + 5472
= 20064 cm
3 Final volume of water in Tank R after 4104 cm
3 of water overflowed
= 20064 - 4104
= 15960 cm
3 Base area of Tank R
= 24 x 19
= 456 cm
2 Height of Tank R
= 15960 ÷ 456
= 35 cm
Answer(s): (a) 14592 cm
2 ; (b) 35 cm