Volume and Surface Area practice [33 marks]
1a. [3 marks]
A metal sphere has a radius 12.7 cm.
Find the volume of the sphere expressing your answer in the form 𝑎 × 10𝑘 , 1 ≤ 𝑎 <
10 and 𝑘 ∈ ℤ.
1b. [3 marks]
The sphere is to be melted down and remoulded into the shape of a cone with a height
of 14.8 cm.
Find the radius of the base of the cone, correct to 2 significant figures.
2a. [1 mark]
A solid glass paperweight consists of a hemisphere of diameter 6 cm on top of a
cuboid with a square base of length 6 cm, as shown in the diagram.
The height of the cuboid, x cm, is equal to the height of the hemisphere.
Write down the value of x.
2b. [3 marks]
Calculate the volume of the paperweight.
2c. [2 marks]
1 cm3 of glass has a mass of 2.56 grams.
Calculate the mass, in grams, of the paperweight.
3a. [2 marks]
A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.
A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is
removed from the top of the larger cone, as shown in the diagram.
Calculate the radius of the base of the cone which has been removed.
3b. [2 marks]
Calculate the curved surface area of the cone which has been removed.
3c. [2 marks]
Calculate the curved surface area of the remaining solid.
4a. [2 marks]
A factory packages coconut water in cone-shaped containers with a base radius of
5.2 cm and a height of 13 cm.
Find the volume of one cone-shaped container.
4b. [2 marks]
Find the slant height of the cone-shaped container.
4c. [3 marks]
Show that the total surface area of the cone-shaped container is 314 cm2, correct to
three significant figures.
4d. [4 marks]
The factory designers are currently investigating whether a cone-shaped container
can be replaced with a cylinder-shaped container with the same radius and the same
total surface area.
Find the height, ℎ, of this cylinder-shaped container.
4e. [4 marks]
The factory director wants to increase the volume of coconut water sold per
container.
State whether or not they should replace the cone-shaped containers with
cylinder‑shaped containers. Justify your conclusion.
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