The figure, not drawn to scale, is made of two connected cubical containers, N and P. Container N is sealed at the top and completely filled to the brim. Container P is
34 filled with 161661 mℓ of water. The height of the water level in Container P is 3 cm higher than that in Container N. Height of Container P is 64 cm. Water is then drained from the container and the height of the water level from the base falls to 33 cm.
- What is the capacity of Container P in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container P = 161661 mℓ
14 of Container P = 161661 ÷ 3 = 53887 mℓ
44 of Container P = 53887 x 4 = 215548 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 215548 mℓ = 215.548 ℓ
(b)
Fraction of Container P not filled
= 1 -
34 =
14 Height of Container P not filled
=
14 x 64 cm
= 16 cm
Height of Container N
= 64 - 16 - 3
= 45 cm
Volume of remaining water in Container N
= 45 x 45 x 33
= 66825 cm
3 Volume of remaining water in Container P
= 64 x 64 x 33
= 135168 cm
3 Total volume of remaining water in the container
= 66825 + 135168
= 201993 cm
3
1 ℓ = 1000 cm
3 201993 cm
3 = 201.993 ℓ
Answer(s): (a) 215.548 ℓ; (b) 201.993 ℓ