Past Paper Example 1
GCSE Jun 2025 3H Q16
4 marks
The diagram shows a solid shape made from a cylinder and a cone.
Work out the vertical height of the cone.
You must show all your working.
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
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
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