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 160455 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 65 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 = 160455 mℓ
15 of Tank Q = 160455 ÷ 3 = 53485 mℓ
55 of Tank Q = 53485 x 5 = 267425 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 267425 mℓ = 267.425 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
35 =
25 Height of Tank Q not filled
=
25 x 65 cm
= 26 cm
Height of Tank P
= 65 - 26 - 1
= 38 cm
Volume of remaining water in Tank P
= 38 x 38 x 28
= 40432 cm
3 Volume of remaining water in Tank Q
= 65 x 65 x 28
= 118300 cm
3 Total volume of remaining water in the tank
= 40432 + 118300
= 158732 cm
3
1 ℓ = 1000 cm
3 158732 cm
3 = 158.732 ℓ
Answer(s): (a) 267.425 ℓ; (b) 158.732 ℓ