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Solutions
12 Videos

A sphere has a radius of 3 cm. What is its volume, to the nearest cubic centimetre?

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Q1

What is the area of the figure, to the nearest square centimetre? Show all steps to your solutions.

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Q2

A circular swimming pool has a diameter of 7.5 m. It is filled to a depth of 1.4 m. What is the volume of water in the pool, to the nearest litre?

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Q3

A conical pile of road salt is 15 m high and has a base diameter of 30 m. How much plastic sheeting is required to cover the pile, to the nearest square metre?

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Q4

What is the length of the unknown side of the triangle, to the nearest tenth of a millimetre?

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Q5

A candle is in the shape of a square-based pyramid.

a) How much wax is needed to create the candle, to the nearest cubic centimetre?

b) How much plastic wrap, to the nearest tenth of a square centimetre, would you need to completely cover the candle? What assumptions did you make?

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Q6

A rectangular cardboard carton is designed to hold six rolls of paper towel that are 28 cm high and 10 cm in diameter. Describe how you would calculate the amount of cardboard required to make this carton.

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Q7

Compare the effects of doubling the radius on the volume of a cylinder and a sphere. Justify your answer with numerical examples.

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Q8

Calculate the surface area of the cone that just fits inside a cylinder with a base radius of 8cm and a height of 10cm. Round to the nearest square centimetre.

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Q9

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Q10

Three tennis balls that measure 8.4 cm in diameter are stacked in a cylindrical can.

a) Determine the minimum volume of the can, to the nearest tenth of a cubic centimetre.

b) Calculate the amount of aluminum required to make the can, including the top and bottom. Round to the nearest square centimetre.

c) The can comes with a plastic lid to be used once the can is opened. Find the amount of plastic required for the lid. Round to the nearest square centimetre.

d) Describe any assumptions you have made.

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Q11

A rectangular carton holds 12 cylindrical cans that each contain three tennis balls, like the ones described in question 11.

a) How much empty space is in each can of tennis balls, to the nearest tenth of a cubic centimetre?

b) Draw a diagram to show the dimensions of the carton.

c) How much empty space is in the carton and cans once the 12 cans are placed in the carton?

d) What is the minimum amount of cardboard necessary to make this carton?

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Q12