8. Conan lives on a farm in Roscommon. He wants to drill his own private well.


Conan drills a cylindrical hole that is 4 metres deep and 2 metres wide.


The soil from the well construction was removed and piled on the ground.


(i) What is the volume of the soil in the pile on the ground? Give your answer to two decimal places.


(ii) If 1 m3 of soil has a mass of 1 500 kg, what


is the mass of the soil removed, to the nearest kilogram?


9. It is important to conserve water. Mr Jones has a leaking tap. In one hour, leaking water fi lls a cylinder of radius 5 cm and height 10 cm.


(i) How many litres of water is this? Give your answer to four decimal places.


(ii) If the tap leaks overnight (12 hours), how many litres of water have been wasted?


Give your answer to four decimal places.


(iii) It takes Mr Jones 7 full days to get the tap repaired. How much water has been lost due to the leak? Assume one day = 24 hours. Give your answer to four decimal places.


1 000 cm3


10. A student measured the outside dimensions of a can of soup. The height was 10·5 cm and the diameter was 7·4 cm. The student calculated the volume to be 452 cm3 nearest whole number.


, to the


(i) Was the student correct? How do you know?


(ii) The label on the can shows the actual volume of soup in the can is 400 ml. Why do you think the manufacturer would not fi ll the can with 452 ml of soup?


= 1 litre


Taking it FURTHER


11. The steel barrel shown has developed a leak.


85.1 cm 57.2 cm


Liquid pours out of the barrel at a rate of 30 litres per hour. (i) Calculate the volume of the barrel. Give your answer to two decimal places.


(ii) How many litres of liquid can the barrel hold? Give your answer to two decimal places. (1 litre = 1 000 cm3


)


(iii) How many cm has the height of the water dropped in 3 hours? Give your answer to the nearest whole number.


(iv) How long, in hours and minutes, will it take for the barrel to be empty?


12. Orange juice is sold in cylindrical cans. A can has a height of 8 cm and a diameter of 7 cm. (i) What is the capacity (volume) of the can to two decimal places.


(ii) What happens to the capacity of the can if the dimensions of the radius and height are swapped? Justify your answer.


(iii) Why do you think this happens?


13. Four cubes of ice with an edge length of 4 cm each placed in a cylindrical glass of water with a radius of 6 cm. (i) What is the volume of one cube of ice?


(ii) Calculate by how many cm the water will rise when all the ice cubes have melted. Give your answer to two decimal places.


14. Ann is making a candle by pouring melted wax into a mould in the shape of a cylinder. The diameter of the cylindrical mould is 6 cm and its height is 8 cm. To get the wax for the candles, Ann melts cubes of wax that are each 3 cm by 3 cm by 3 cm.


How many full wax cubes will Ann need to make the candle?


Section B Moving forward 279


17 Area, volume and surface area


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