The figure, not drawn to scale, is made of two connected cubical containers, Q and R. Container Q is sealed at the top and completely filled to the brim. Container R is
34 filled with 113952 mℓ of water. The height of the water level in Container R is 1 cm higher than that in Container Q. Height of Container R is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.
- What is the capacity of Container R in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container R = 113952 mℓ
14 of Container R = 113952 ÷ 3 = 37984 mℓ
44 of Container R = 37984 x 4 = 151936 mℓ
1 ℓ = 1000 mℓ
Capacity of Container R = 151936 mℓ = 151.936 ℓ
(b)
Fraction of Container R not filled
= 1 -
34 =
14 Height of Container R not filled
=
14 x 68 cm
= 17 cm
Height of Container Q
= 68 - 17 - 1
= 50 cm
Volume of remaining water in Container Q
= 50 x 50 x 37
= 92500 cm
3 Volume of remaining water in Container R
= 68 x 68 x 37
= 171088 cm
3 Total volume of remaining water in the container
= 92500 + 171088
= 263588 cm
3
1 ℓ = 1000 cm
3 263588 cm
3 = 263.588 ℓ
Answer(s): (a) 151.936 ℓ; (b) 263.588 ℓ