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
25 filled with 101310 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 67 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Tank Q in litres?
- What is the volume of water in the tank now in litres?
(a)
25 of Tank Q = 101310 mℓ
15 of Tank Q = 101310 ÷ 2 = 50655 mℓ
55 of Tank Q = 50655 x 5 = 253275 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 253275 mℓ = 253.275 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
25 =
35 Height of Tank Q not filled
=
35 x 67 cm
= 40.2 cm
Height of Tank P
= 67 - 40.2 - 4
= 22.8 cm
Volume of remaining water in Tank P
= 22.8 x 22.8 x 25
= 12996 cm
3 Volume of remaining water in Tank Q
= 67 x 67 x 25
= 112225 cm
3 Total volume of remaining water in the tank
= 12996 + 112225
= 125221 cm
3
1 ℓ = 1000 cm
3 125221 cm
3 = 125.221 ℓ
Answer(s): (a) 253.275 ℓ; (b) 125.221 ℓ