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 149168 mℓ of water. The height of the water level in Tank R is 5 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 23 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 = 149168 mℓ
13 of Tank R = 149168 ÷ 2 = 74584 mℓ
33 of Tank R = 74584 x 3 = 223752 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank R = 223752 mℓ = 223.752 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 - 5
= 37 cm
Volume of remaining water in Tank Q
= 37 x 37 x 23
= 31487 cm
3 Volume of remaining water in Tank R
= 63 x 63 x 23
= 91287 cm
3 Total volume of remaining water in the tank
= 31487 + 91287
= 122774 cm
3
1 ℓ = 1000 cm
3 122774 cm
3 = 122.774 ℓ
Answer(s): (a) 223.752 ℓ; (b) 122.774 ℓ