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5.16F Spheres and Cones: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the formula for the volume V of a sphere in terms of its radius r.

(Total for Question 1 is 1 mark)

A small ball has radius 6 cm. Calculate its volume. Give your answer in terms of π.

(Total for Question 2 is 1 mark)

The volume of a sphere is 36 π cm³. Work out its radius in cm. Give your answer in exact form.

(Total for Question 3 is 2 marks)

A cone has radius 5 cm and height 12 cm. Calculate its volume. Give your answer to 1 decimal place. Use π = 3.14159265 or your calculator's π key.

(Total for Question 4 is 2 marks)

A toy cone and a toy sphere are made from the same material. The cone has radius 4 cm and height 9 cm. The sphere has radius 6 cm. Which object has the larger volume and by how much? Give your answer to 1 decimal place.

(Total for Question 5 is 3 marks)

A right circular cone has sloping edge (the slant height) 13 cm and radius 5 cm. Calculate the height of the cone. Give your answer in cm.

(Total for Question 6 is 3 marks)

A hemisphere is half of a sphere. A hemisphere has radius 7 cm. Calculate its curved surface area (not including the base). Give your answer to 1 decimal place. Use the curved surface area of a sphere = 4 π r², so hemisphere curved area = 2 π r².

(Total for Question 7 is 4 marks)

A cone and a cylinder have the same radius 3 cm. The cone has height 8 cm and the cylinder has height 8 cm. Work out the total volume of the two solids. Give your answer in terms of π.

(Total for Question 8 is 6 marks)

A solid is made by placing a sphere of radius 4 cm on top of a cone whose base radius is 4 cm and height 6 cm so that the sphere touches the cone along the circle of the cone's top. Calculate the total volume of the solid. Give your answer to 1 decimal place.

(Total for Question 9 is 8 marks)

Mark scheme · 5.16F Spheres and Cones: Foundation Tier Practice

Question 1

B1 V = (4/3) π r³ or equivalent cao
Answer: V = (4/3) π r³

Question 2

B1 288 π cm³ cao
Answer: 288 π cm³

Question 3

M1 use (4/3) π r³ = 36 π and cancel π then r³ = 27
A1 r = 3 cm cao
Answer: 3 cm

Question 4

M1 use V = (1/3) π r² h with r=5, h=12
A1 314.2 cm³ awrt
Answer: 314.2 cm³

Question 5

M1 calculate cone volume: (1/3) π (4²) * 9 = 48 π
M1 calculate sphere volume: (4/3) π * 6³ = 288 π
A1 sphere larger by 240 π = 754.0 cm³ awrt
Answer: The sphere is larger by 754.0 cm³ (to 1 d.p.)

Question 6

M1 use Pythagoras: height² + 5² = 13²
M1 compute height² = 169 - 25 = 144
A1 height = 12 cm cao
Answer: 12 cm

Question 7

M1 use hemisphere curved area = 2 π r² with r=7
M1 compute 2 * π * 49 = 98 π
M1 convert to decimal using π: 98 * π = 307.87608...
A1 307.9 cm² awrt
Answer: 307.9 cm²

Question 8

M1 find r²: 3² = 9
M1 cylinder volume method: V = π r² h, so 9 * 8 = 72, cylinder = 72 π
M1 cone method: V = (1/3) π r² h, so (1/3) * 9 * 8 = 24, cone = 24 π
M1 write cone volume = 24 π and cylinder = 72 π
A1 add volumes: 72 π + 24 π = 96 π
A1 96 π cm³ cao
Answer: 96 π cm³

Question 9

M1 compute sphere volume formula substitution: (4/3) π * 4³
M1 simplify sphere volume to (256/3) π
M1 compute cone volume formula substitution: (1/3) π * 4² * 6
M1 simplify cone volume to 32 π
M1 convert sphere volume to decimal: (256/3) π = 268.082... cm³
M1 convert cone volume to decimal: 32 π = 100.531... cm³
M1 add decimal volumes: 268.082... + 100.531... = 368.613...
A1 368.6 cm³ awrt
Answer: 368.6 cm³

Spheres and Cones: Foundation Tier Practice - Worksheets, Questions and Revision