GCSE Maths Practice: surface-area

Question 3 of 10

This question introduces calculating the curved surface area of a cone using radius and slant height.

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\( \begin{array}{l}\text{Find the curved surface area of a cone with} \\ \text{radius } 5\,\text{cm} \text{ and slant height } 12\,\text{cm}, \\ \text{giving your answer in terms of } \pi.\end{array} \)

Choose one option:

Use slant height, not vertical height. Multiply by π. Check units.

To calculate the curved surface area (CSA) of a cone, use CSA = π r l, where r is the radius of the base and l is the slant height. The slant height is the diagonal distance along the side from apex to the edge of the base. For a cone with radius 5 cm and slant height 12 cm, CSA = π × 5 × 12 = 60π cm². Understanding the difference between slant height and vertical height is critical. This formula applies to many real-world problems, including funnels, ice-cream cones, and conical roofs. Practice visualizing the slant height and applying the formula correctly.