The figure, not drawn to scale, is made of two connected cubical tanks, M and N. Tank M is sealed at the top and completely filled to the brim. Tank N is
23 filled with 113794 mℓ of water. The height of the water level in Tank N is 3 cm higher than that in Tank M. Height of Tank N is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Tank N in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank N = 113794 mℓ
13 of Tank N = 113794 ÷ 2 = 56897 mℓ
33 of Tank N = 56897 x 3 = 170691 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 170691 mℓ = 170.691 ℓ
(b)
Fraction of Tank N not filled
= 1 -
23 =
13 Height of Tank N not filled
=
13 x 57 cm
= 19 cm
Height of Tank M
= 57 - 19 - 3
= 35 cm
Volume of remaining water in Tank M
= 35 x 35 x 26
= 31850 cm
3 Volume of remaining water in Tank N
= 57 x 57 x 26
= 84474 cm
3 Total volume of remaining water in the tank
= 31850 + 84474
= 116324 cm
3
1 ℓ = 1000 cm
3 116324 cm
3 = 116.324 ℓ
Answer(s): (a) 170.691 ℓ; (b) 116.324 ℓ