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
34 filled with 104181 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 56 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.
- What is the capacity of Tank Q in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank Q = 104181 mℓ
14 of Tank Q = 104181 ÷ 3 = 34727 mℓ
44 of Tank Q = 34727 x 4 = 138908 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Q = 138908 mℓ = 138.908 ℓ
(b)
Fraction of Tank Q not filled
= 1 -
34 =
14 Height of Tank Q not filled
=
14 x 56 cm
= 14 cm
Height of Tank P
= 56 - 14 - 1
= 41 cm
Volume of remaining water in Tank P
= 41 x 41 x 34
= 57154 cm
3 Volume of remaining water in Tank Q
= 56 x 56 x 34
= 106624 cm
3 Total volume of remaining water in the tank
= 57154 + 106624
= 163778 cm
3
1 ℓ = 1000 cm
3 163778 cm
3 = 163.778 ℓ
Answer(s): (a) 138.908 ℓ; (b) 163.778 ℓ