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 106340 mℓ of water. The height of the water level in Tank R is 4 cm higher than that in Tank Q. Height of Tank R is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 35 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 = 106340 mℓ
13 of Tank R = 106340 ÷ 2 = 53170 mℓ
33 of Tank R = 53170 x 3 = 159510 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank R = 159510 mℓ = 159.51 ℓ
(b)
Fraction of Tank R not filled
= 1 -
23 =
13 Height of Tank R not filled
=
13 x 69 cm
= 23 cm
Height of Tank Q
= 69 - 23 - 4
= 42 cm
Volume of remaining water in Tank Q
= 42 x 42 x 35
= 61740 cm
3 Volume of remaining water in Tank R
= 69 x 69 x 35
= 166635 cm
3 Total volume of remaining water in the tank
= 61740 + 166635
= 228375 cm
3
1 ℓ = 1000 cm
3 228375 cm
3 = 228.375 ℓ
Answer(s): (a) 159.51 ℓ; (b) 228.375 ℓ