The figure, not drawn to scale, is made of two connected cubical tanks, L and M. Tank L is sealed at the top and completely filled to the brim. Tank M is
45 filled with 130064 mℓ of water. The height of the water level in Tank M is 5 cm higher than that in Tank L. Height of Tank M is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.
- What is the capacity of Tank M in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank M = 130064 mℓ
15 of Tank M = 130064 ÷ 4 = 32516 mℓ
55 of Tank M = 32516 x 5 = 162580 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank M = 162580 mℓ = 162.58 ℓ
(b)
Fraction of Tank M not filled
= 1 -
45 =
15 Height of Tank M not filled
=
15 x 60 cm
= 12 cm
Height of Tank L
= 60 - 12 - 5
= 43 cm
Volume of remaining water in Tank L
= 43 x 43 x 30
= 55470 cm
3 Volume of remaining water in Tank M
= 60 x 60 x 30
= 108000 cm
3 Total volume of remaining water in the tank
= 55470 + 108000
= 163470 cm
3
1 ℓ = 1000 cm
3 163470 cm
3 = 163.47 ℓ
Answer(s): (a) 162.58 ℓ; (b) 163.47 ℓ