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AQA GCSE · Question 07.1 · Geometry and Measures
Here is a cone.
Curved surface area of a cone = πrl, where r is the radius and l is the slant height.
Beth tries to work out the curved surface area in terms of π.
Her working is:
Curved surface area of the cone = π × 5 × 12 = 60π cm²
What mistake has she made?
Here is a cone.
Curved surface area of a cone = πrl, where r is the radius and l is the slant height.
Beth tries to work out the curved surface area in terms of π.
Her working is:
Curved surface area of the cone = π × 5 × 12 = 60π cm²
What mistake has she made?
How to approach this question
Look at the formula for the curved surface area of a cone: πrl. Identify what `r` and `l` represent. Compare the values given in the diagram for radius, perpendicular height, and slant height. Check which values Beth used in her calculation.
Full Answer
Beth has used the perpendicular height (12 cm) instead of the slant height (13 cm) in the formula.
The formula for the curved surface area of a cone is A = πrl.
In this formula:
- `r` is the radius of the circular base. From the diagram, r = 5 cm.
- `l` is the slant height, which is the distance from the apex (the tip) to a point on the circumference of the base. From the diagram, l = 13 cm.
The value 12 cm is the perpendicular height (`h`) of the cone.
Beth's calculation was π × 5 × 12. She correctly used r = 5, but she incorrectly used h = 12 for the slant height `l`. She should have used l = 13.
Common mistakes
✗ A vague answer like "She used the wrong number".
✗ Confusing radius and diameter.
✗ Stating that she should have used Pythagoras' theorem (this isn't the mistake in her application of the formula, although the numbers do form a Pythagorean triple).
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