The figure, not drawn to scale, is made of two connected cubical tanks, Z and A. Tank Z is sealed at the top and completely filled to the brim. Tank A is
23 filled with 155498 mℓ of water. The height of the water level in Tank A is 1 cm higher than that in Tank Z. Height of Tank A is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Tank A in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank A = 155498 mℓ
13 of Tank A = 155498 ÷ 2 = 77749 mℓ
33 of Tank A = 77749 x 3 = 233247 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank A = 233247 mℓ = 233.247 ℓ
(b)
Fraction of Tank A not filled
= 1 -
23 =
13 Height of Tank A not filled
=
13 x 69 cm
= 23 cm
Height of Tank Z
= 69 - 23 - 1
= 45 cm
Volume of remaining water in Tank Z
= 45 x 45 x 39
= 78975 cm
3 Volume of remaining water in Tank A
= 69 x 69 x 39
= 185679 cm
3 Total volume of remaining water in the tank
= 78975 + 185679
= 264654 cm
3
1 ℓ = 1000 cm
3 264654 cm
3 = 264.654 ℓ
Answer(s): (a) 233.247 ℓ; (b) 264.654 ℓ