An empty tank measures 50 cm by 20 cm by 35 cm. 3 wooden 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 5 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 2 wooden cubes are removed?
(a)
Volume of the tank
= 50 x 20 x 35
= 35000 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
= 35000 - 3000
= 32000 cm
3
1 ℓ = 1000 cm
3
5 ℓ = 5000 cm
3
Time taken to fill the tank
= 32000 ÷ 5000
= 6.4 min
(b)
Volume of 2 cubes
= 2 x 1000
= 2000 cm
3 Base area of the tank
= 50 x 20
= 1000 cm
2 Decrease in the depth of water
= 2000 ÷ 1000
= 2 cm
Depth of water after removing 2 cubes
= 35 - 2
= 33 cm
Answer(s): (a) 6.4 min; (b) 33 cm