The figure, not drawn to scale, is made of two connected cubical tanks, P and Q. Tank P is sealed at the top and completely filled to the brim. Tank Q is
35 filled with 105990 mℓ of water. The height of the water level in Tank Q is 4 cm higher than that in Tank P. Height of Tank Q is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 28 cm.
- What is the capacity of Tank Q in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank Q = 105990 mℓ
15 of Tank Q = 105990 ÷ 3 = 35330 mℓ
55 of Tank Q = 35330 x 5 = 176650 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 176650 mℓ = 176.65 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
35 =
25 Height of Tank Q not filled
=
25 x 60 cm
= 24 cm
Height of Tank P
= 60 - 24 - 4
= 32 cm
Volume of remaining water in Tank P
= 32 x 32 x 28
= 28672 cm
3 Volume of remaining water in Tank Q
= 60 x 60 x 28
= 100800 cm
3 Total volume of remaining water in the tank
= 28672 + 100800
= 129472 cm
3
1 ℓ = 1000 cm
3 129472 cm
3 = 129.472 ℓ
Answer(s): (a) 176.65 ℓ; (b) 129.472 ℓ