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Spheres, cones and cylinders

Free Printable Spheres, cones and cylinders PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 8+)

Download free spheres, cones and cylinders worksheets (PDF), GCSE maths past paper questions and worked solutions for Spheres, cones and cylinders (8N). This is a Grade 8+ geometry topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths4Everyone, Maths DIY, Dr Austin, 1st Class Maths, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our spheres, cones and cylinders revision notes and worked examples with diagrams, try real GCSE past paper spheres, cones and cylinders questions with step-by-step solutions, or download a PDF of all spheres, cones and cylinders worksheet links.

Free Spheres, cones and cylinders PDF Worksheets & Answers

Grade 8+ • Topic 8N
Resource Questions Answers
Practice worksheet & worked solutions
 Qs Ans
GCSE 9–1 practice booklet & solutions
 Qs Ans
Exam-style booklet & solutions
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
 Qs Ans
Practice grid / worksheet & answers
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GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Grade 8+ topics
8A - Quad. sim. equations8B - Transforming graphs y=f(x)
8C - Algebraic proof8D - Completing the square
8E - Quadratic inequalities8F - Quadratic sequences
8G - Velocity time graphs8H - Circles and tangents
8J - Circle theorem proof8K - Vector proof
8L - Probability equation questions8M - Invariant points
8N - Spheres, cones and cylinders8P - Volume of a frustum
GCSE Maths Grade 8+ Revision Notes & Method

Guide to Spheres, cones and cylinders: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Key 3D curved solid formulas: Cylinder volume = πr2h, curved surface area = 2πrh; Sphere volume = 43πr3, surface area = 4πr2; Cone volume = 13πr2h, curved surface area = πrl (where slant height l = √(r2 + h2)).

For a solid hemisphere or solid cone, remember to include the flat circular base (+πr2), so the total surface area of a solid hemisphere is 2πr2 + πr2 = 3πr2. When melting and recasting shapes, equate their exact volumes in terms of π so π cancels cleanly.

Example 1: Find the exact total surface area of a solid cone with base radius 5 cm and vertical height 12 cm.

12 5 cm l = 13

Solution:

l = √(52 + 122) = 13 cm
CSA + Base = π(5)(13) + π(5)2 = 65π + 25π = 90π cm2

Example 2: A metal sphere of radius 6 cm is melted down to form a cylinder of radius 4 cm. Find the height h of the cylinder.

6 4 h

Solution:

Vsphere = 43π(6)3 = 288π;  Vcyl = π(4)2h = 16πh
16πh = 288π ⇒ h = 288 ÷ 16 = 18 cm
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Spheres, cones and cylinders Questions & Answers

Past Paper Example 1 GCSE Jun 2022 2H Q17 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
A solid cone is joined to a solid hemisphere to make the solid **T** shown below.
y cm7 cmVolume of sphere =43πr3rVolume of cone =13πr2hrlh
The diameter of the base of the cone is 7 cm.
The diameter of the hemisphere is 7 cm.
The total volume of **T** is 120π cm3
The total height of **T** is y cm.
(a) Calculate the value of y.
Give your answer correct to 3 significant figures. [4 marks]
(b) explain the effect this would have on your answer to part (a). [1 mark]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
r = 3.5 cm M1
Hemisphere volume = (2/3)π(3.5³) = (343/12)π M1
Cone volume = (1/3)π(3.5²)(y – 3.5) = (49/12)π(y – 3.5) M1
Total: 343/12 + 49/12(y – 3.5) = 120 ⇒ y – 3.5 = 1097/49 ≈ 22.388 ⇒ y ≈ 25.888 → 25.9 A1
Answer (a): y = 25.9
Part (b) Solution:
The value of y (the total height) would decrease
Answer (b): The value of y (the total height) would decrease
Past Paper Example 2 GCSE May 2019 1H Q15 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a solid shape.
The shape is a cone on top of a hemisphere.
6 cm10 cmVolume of a cone =13πr2hrhVolume of a sphere =43πr3r
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm.
The total volume of the shape is kπ cm3, where k is an integer.
Work out the value of k.
Worked Solution & Mark Scheme (4 marks)
r = 6 ÷ 2 = 3 cm M1
Volume of cone = 1/3 × π × 3² × 10 = 30π M1
Volume of hemisphere = 2/3 × π × 3³ = 18π M1
Total volume = 30π + 18π = 48π ⇒ k = 48 A1
Answer: k = 48
Past Paper Example 3 GCSE Jun 2025 3H Q16 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a solid shape made from a cylinder and a cone.
8 cmVolume of cone = ⅓ π r2hrh
Work out the vertical height of the cone.
You must show all your working.
The cone has a base radius of 8 cm.
The cylinder has a radius of 8 cm.
The vertical height of the cone is three times the height of the cylinder.
The volume of the solid shape is 640π cm3
Worked Solution & Mark Scheme (4 marks)
(The volume of a cylinder is πr²h)
Let cylinder height = H M1
Cone height h = 3H
Radius r = 8 cm M1
Volume of cylinder = π r² H = π × 8² × H = 64π H
Volume of cone = 1/3 π r² h = 1/3 π × 8² × 3H = 64π H M1
Total volume = 64π H + 64π H = 128π H = 640π ⇒ H = 640 ÷ 128 = 5 cm
Height of cone h = 3 × 5 = 15 cm. A1
Answer: 15 cm

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