The figure, not drawn to scale, is made of two connected cubical tanks, R and S. Tank R is sealed at the top and completely filled to the brim. Tank S is
35 filled with 109770 mℓ of water. The height of the water level in Tank S is 3 cm higher than that in Tank R. Height of Tank S is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.
- What is the capacity of Tank S in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank S = 109770 mℓ
15 of Tank S = 109770 ÷ 3 = 36590 mℓ
55 of Tank S = 36590 x 5 = 182950 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank S = 182950 mℓ = 182.95 ℓ
(b)
Fraction of Tank S not filled
= 1 -
35 =
25 Height of Tank S not filled
=
25 x 65 cm
= 26 cm
Height of Tank R
= 65 - 26 - 3
= 36 cm
Volume of remaining water in Tank R
= 36 x 36 x 30
= 38880 cm
3 Volume of remaining water in Tank S
= 65 x 65 x 30
= 126750 cm
3 Total volume of remaining water in the tank
= 38880 + 126750
= 165630 cm
3
1 ℓ = 1000 cm
3 165630 cm
3 = 165.63 ℓ
Answer(s): (a) 182.95 ℓ; (b) 165.63 ℓ