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 102200 mℓ of water. The height of the water level in Tank L is 5 cm higher than that in Tank K. Height of Tank L is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 23 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 = 102200 mℓ
15 of Tank L = 102200 ÷ 4 = 25550 mℓ
55 of Tank L = 25550 x 5 = 127750 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank L = 127750 mℓ = 127.75 ℓ
(b)
Fraction of Tank L not filled
= 1 -
45 =
15 Height of Tank L not filled
=
15 x 60 cm
= 12 cm
Height of Tank K
= 60 - 12 - 5
= 43 cm
Volume of remaining water in Tank K
= 43 x 43 x 23
= 42527 cm
3 Volume of remaining water in Tank L
= 60 x 60 x 23
= 82800 cm
3 Total volume of remaining water in the tank
= 42527 + 82800
= 125327 cm
3
1 ℓ = 1000 cm
3 125327 cm
3 = 125.327 ℓ
Answer(s): (a) 127.75 ℓ; (b) 125.327 ℓ