Tank Y is a cubical container of edge 29 cm. It is completely filled with water. Tank Z is a rectangular tank measuring 45 cm by 25 cm by 27 cm. It is filled with water flowing from a tap at a rate of 0.1 ℓ per minute. 10 minutes later, the tap is turned off.
- Find the volume of water in Tank Z after 10 minutes. Give your answer in litres.
- All the water in Tank Y is then poured into Tank Z without spilling. How much more water is needed to fill Tank Z completely? Give your answer in litres.
(a)
Volume of water in Tank Z filled by the tap
= 10 x 0.1
= 1 ℓ
Volume of water poured into the Tank Z from Tank Y
= 29 x 29 x 29
= 24389 mℓ
1000 mℓ = 1 ℓ
24389 mℓ = 24389 ÷ 1000 = 24.389 ℓ
Volume of Tank Z
= 45 x 25 x 27
= 30375 mℓ
30375 mℓ = 30375 ÷ 1000 = 30.375 ℓ
Volume of more water to fill Tank Z
= 30.375 - 24.389 - 1
= 4.986 ℓ
Answer(s): (a) 1 ℓ; (b) 4.986 ℓ