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 187648 mℓ of water. The height of the water level in Tank Q is 2 cm higher than that in Tank P. Height of Tank Q is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 23 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 = 187648 mℓ
13 of Tank Q = 187648 ÷ 2 = 93824 mℓ
33 of Tank Q = 93824 x 3 = 281472 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 281472 mℓ = 281.472 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
23 =
13 Height of Tank Q not filled
=
13 x 69 cm
= 23 cm
Height of Tank P
= 69 - 23 - 2
= 44 cm
Volume of remaining water in Tank P
= 44 x 44 x 23
= 44528 cm
3 Volume of remaining water in Tank Q
= 69 x 69 x 23
= 109503 cm
3 Total volume of remaining water in the tank
= 44528 + 109503
= 154031 cm
3
1 ℓ = 1000 cm
3 154031 cm
3 = 154.031 ℓ
Answer(s): (a) 281.472 ℓ; (b) 154.031 ℓ