The figure, not drawn to scale, is made of two connected cubical containers, K and L. Container K is sealed at the top and completely filled to the brim. Container L is
45 filled with 116172 mℓ of water. The height of the water level in Container L is 5 cm higher than that in Container K. Height of Container L is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.
- What is the capacity of Container L in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container L = 116172 mℓ
15 of Container L = 116172 ÷ 4 = 29043 mℓ
55 of Container L = 29043 x 5 = 145215 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 145215 mℓ = 145.215 ℓ
(b)
Fraction of Container L not filled
= 1 -
45 =
15 Height of Container L not filled
=
15 x 65 cm
= 13 cm
Height of Container K
= 65 - 13 - 5
= 47 cm
Volume of remaining water in Container K
= 47 x 47 x 29
= 64061 cm
3 Volume of remaining water in Container L
= 65 x 65 x 29
= 122525 cm
3 Total volume of remaining water in the container
= 64061 + 122525
= 186586 cm
3
1 ℓ = 1000 cm
3 186586 cm
3 = 186.586 ℓ
Answer(s): (a) 145.215 ℓ; (b) 186.586 ℓ