The figure, not drawn to scale, is made of two connected cubical tanks, Q and R. Tank Q is sealed at the top and completely filled to the brim. Tank R is
23 filled with 162348 mℓ of water. The height of the water level in Tank R is 2 cm higher than that in Tank Q. Height of Tank R is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.
- What is the capacity of Tank R in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank R = 162348 mℓ
13 of Tank R = 162348 ÷ 2 = 81174 mℓ
33 of Tank R = 81174 x 3 = 243522 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank R = 243522 mℓ = 243.522 ℓ
(b)
Fraction of Tank R not filled
= 1 -
23 =
13 Height of Tank R not filled
=
13 x 63 cm
= 21 cm
Height of Tank Q
= 63 - 21 - 2
= 40 cm
Volume of remaining water in Tank Q
= 40 x 40 x 36
= 57600 cm
3 Volume of remaining water in Tank R
= 63 x 63 x 36
= 142884 cm
3 Total volume of remaining water in the tank
= 57600 + 142884
= 200484 cm
3
1 ℓ = 1000 cm
3 200484 cm
3 = 200.484 ℓ
Answer(s): (a) 243.522 ℓ; (b) 200.484 ℓ