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
23 filled with 104606 mℓ of water. The height of the water level in Tank Q is 1 cm higher than that in Tank P. Height of Tank Q is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 38 cm.
- What is the capacity of Tank Q in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank Q = 104606 mℓ
13 of Tank Q = 104606 ÷ 2 = 52303 mℓ
33 of Tank Q = 52303 x 3 = 156909 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 156909 mℓ = 156.909 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
23 =
13 Height of Tank Q not filled
=
13 x 57 cm
= 19 cm
Height of Tank P
= 57 - 19 - 1
= 37 cm
Volume of remaining water in Tank P
= 37 x 37 x 38
= 52022 cm
3 Volume of remaining water in Tank Q
= 57 x 57 x 38
= 123462 cm
3 Total volume of remaining water in the tank
= 52022 + 123462
= 175484 cm
3
1 ℓ = 1000 cm
3 175484 cm
3 = 175.484 ℓ
Answer(s): (a) 156.909 ℓ; (b) 175.484 ℓ