The figure, not drawn to scale, is made of two connected cubical tanks, N and P. Tank N is sealed at the top and completely filled to the brim. Tank P is
35 filled with 159087 mℓ of water. The height of the water level in Tank P is 2 cm higher than that in Tank N. Height of Tank P is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 28 cm.
- What is the capacity of Tank P in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank P = 159087 mℓ
15 of Tank P = 159087 ÷ 3 = 53029 mℓ
55 of Tank P = 53029 x 5 = 265145 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank P = 265145 mℓ = 265.145 ℓ
(b)
Fraction of Tank P not filled
= 1 -
35 =
25 Height of Tank P not filled
=
25 x 70 cm
= 28 cm
Height of Tank N
= 70 - 28 - 2
= 40 cm
Volume of remaining water in Tank N
= 40 x 40 x 28
= 44800 cm
3 Volume of remaining water in Tank P
= 70 x 70 x 28
= 137200 cm
3 Total volume of remaining water in the tank
= 44800 + 137200
= 182000 cm
3
1 ℓ = 1000 cm
3 182000 cm
3 = 182 ℓ
Answer(s): (a) 265.145 ℓ; (b) 182 ℓ