The figure, not drawn to scale, is made of two connected cubical tanks, K and L. Tank K is sealed at the top and completely filled to the brim. Tank L is
45 filled with 103028 mℓ of water. The height of the water level in Tank L is 3 cm higher than that in Tank K. Height of Tank L is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Tank L in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank L = 103028 mℓ
15 of Tank L = 103028 ÷ 4 = 25757 mℓ
55 of Tank L = 25757 x 5 = 128785 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank L = 128785 mℓ = 128.785 ℓ
(b)
Fraction of Tank L not filled
= 1 -
45 =
15 Height of Tank L not filled
=
15 x 66 cm
= 13.2 cm
Height of Tank K
= 66 - 13.2 - 3
= 49.8 cm
Volume of remaining water in Tank K
= 49.8 x 49.8 x 25
= 62001 cm
3 Volume of remaining water in Tank L
= 66 x 66 x 25
= 108900 cm
3 Total volume of remaining water in the tank
= 62001 + 108900
= 170901 cm
3
1 ℓ = 1000 cm
3 170901 cm
3 = 170.901 ℓ
Answer(s): (a) 128.785 ℓ; (b) 170.901 ℓ