The figure, not drawn to scale, is made of two connected cubical tanks, J and K. Tank J is sealed at the top and completely filled to the brim. Tank K is
23 filled with 109332 mℓ of water. The height of the water level in Tank K is 2 cm higher than that in Tank J. Height of Tank K is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Tank K in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank K = 109332 mℓ
13 of Tank K = 109332 ÷ 2 = 54666 mℓ
33 of Tank K = 54666 x 3 = 163998 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank K = 163998 mℓ = 163.998 ℓ
(b)
Fraction of Tank K not filled
= 1 -
23 =
13 Height of Tank K not filled
=
13 x 63 cm
= 21 cm
Height of Tank J
= 63 - 21 - 2
= 40 cm
Volume of remaining water in Tank J
= 40 x 40 x 27
= 43200 cm
3 Volume of remaining water in Tank K
= 63 x 63 x 27
= 107163 cm
3 Total volume of remaining water in the tank
= 43200 + 107163
= 150363 cm
3
1 ℓ = 1000 cm
3 150363 cm
3 = 150.363 ℓ
Answer(s): (a) 163.998 ℓ; (b) 150.363 ℓ