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
25 filled with 106770 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 65 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.
- What is the capacity of Tank R in litres?
- What is the volume of water in the tank now in litres?
(a)
25 of Tank R = 106770 mℓ
15 of Tank R = 106770 ÷ 2 = 53385 mℓ
55 of Tank R = 53385 x 5 = 266925 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank R = 266925 mℓ = 266.925 ℓ
(b)
Fraction of Tank R not filled
= 1 -
25 =
35 Height of Tank R not filled
=
35 x 65 cm
= 39 cm
Height of Tank Q
= 65 - 39 - 2
= 24 cm
Volume of remaining water in Tank Q
= 24 x 24 x 29
= 16704 cm
3 Volume of remaining water in Tank R
= 65 x 65 x 29
= 122525 cm
3 Total volume of remaining water in the tank
= 16704 + 122525
= 139229 cm
3
1 ℓ = 1000 cm
3 139229 cm
3 = 139.229 ℓ
Answer(s): (a) 266.925 ℓ; (b) 139.229 ℓ