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 102846 mℓ of water. The height of the water level in Tank Q is 3 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 31 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 = 102846 mℓ
15 of Tank Q = 102846 ÷ 2 = 51423 mℓ
55 of Tank Q = 51423 x 5 = 257115 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 257115 mℓ = 257.115 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
25 =
35 Height of Tank Q not filled
=
35 x 65 cm
= 39 cm
Height of Tank P
= 65 - 39 - 3
= 23 cm
Volume of remaining water in Tank P
= 23 x 23 x 31
= 16399 cm
3 Volume of remaining water in Tank Q
= 65 x 65 x 31
= 130975 cm
3 Total volume of remaining water in the tank
= 16399 + 130975
= 147374 cm
3
1 ℓ = 1000 cm
3 147374 cm
3 = 147.374 ℓ
Answer(s): (a) 257.115 ℓ; (b) 147.374 ℓ