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
34 filled with 142566 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 62 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Tank Q in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank Q = 142566 mℓ
14 of Tank Q = 142566 ÷ 3 = 47522 mℓ
44 of Tank Q = 47522 x 4 = 190088 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 190088 mℓ = 190.088 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
34 =
14 Height of Tank Q not filled
=
14 x 62 cm
= 15.5 cm
Height of Tank P
= 62 - 15.5 - 4
= 42.5 cm
Volume of remaining water in Tank P
= 42.5 x 42.5 x 40
= 72250 cm
3 Volume of remaining water in Tank Q
= 62 x 62 x 40
= 153760 cm
3 Total volume of remaining water in the tank
= 72250 + 153760
= 226010 cm
3
1 ℓ = 1000 cm
3 226010 cm
3 = 226.01 ℓ
Answer(s): (a) 190.088 ℓ; (b) 226.01 ℓ