An empty tank measures 60 cm by 25 cm by 45 cm. 3 rubber cubes each of edge 10 cm, are placed in the tank. The tank is then filled with water flowing from a tap at a rate of 12 ℓ per minute.
- How long will it take to fill up the tank? Express your answer in min.
- What will be the depth of the water in the tank after 3 rubber cubes are removed?
(a)
Volume of the tank
= 60 x 25 x 45
= 67500 cm
3 Volume of 1 cube
= 10 x 10 x 10
= 1000 cm
3 Volume of 3 cubes
= 3 x 1000
= 3000 cm
3 Volume of water needed to fill the tank
= 67500 - 3000
= 64500 cm
3
1 ℓ = 1000 cm
3
12 ℓ = 12000 cm
3
Time taken to fill the tank
= 64500 ÷ 12000
= 5.375 min
(b)
Volume of 3 cubes
= 3 x 1000
= 3000 cm
3 Base area of the tank
= 60 x 25
= 1500 cm
2 Decrease in the depth of water
= 3000 ÷ 1500
= 2 cm
Depth of water after removing 3 cubes
= 45 - 2
= 43 cm
Answer(s): (a) 5.375 min; (b) 43 cm