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
34 filled with 136737 mℓ of water. The height of the water level in Tank P is 5 cm higher than that in Tank N. Height of Tank P is 64 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.
- What is the capacity of Tank P in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank P = 136737 mℓ
14 of Tank P = 136737 ÷ 3 = 45579 mℓ
44 of Tank P = 45579 x 4 = 182316 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank P = 182316 mℓ = 182.316 ℓ
(b)
Fraction of Tank P not filled
= 1 -
34 =
14 Height of Tank P not filled
=
14 x 64 cm
= 16 cm
Height of Tank N
= 64 - 16 - 5
= 43 cm
Volume of remaining water in Tank N
= 43 x 43 x 36
= 66564 cm
3 Volume of remaining water in Tank P
= 64 x 64 x 36
= 147456 cm
3 Total volume of remaining water in the tank
= 66564 + 147456
= 214020 cm
3
1 ℓ = 1000 cm
3 214020 cm
3 = 214.02 ℓ
Answer(s): (a) 182.316 ℓ; (b) 214.02 ℓ