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 113175 mℓ of water. The height of the water level in Tank P is 4 cm higher than that in Tank N. Height of Tank P is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 34 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 = 113175 mℓ
14 of Tank P = 113175 ÷ 3 = 37725 mℓ
44 of Tank P = 37725 x 4 = 150900 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank P = 150900 mℓ = 150.9 ℓ
(b)
Fraction of Tank P not filled
= 1 -
34 =
14 Height of Tank P not filled
=
14 x 60 cm
= 15 cm
Height of Tank N
= 60 - 15 - 4
= 41 cm
Volume of remaining water in Tank N
= 41 x 41 x 34
= 57154 cm
3 Volume of remaining water in Tank P
= 60 x 60 x 34
= 122400 cm
3 Total volume of remaining water in the tank
= 57154 + 122400
= 179554 cm
3
1 ℓ = 1000 cm
3 179554 cm
3 = 179.554 ℓ
Answer(s): (a) 150.9 ℓ; (b) 179.554 ℓ