Shape and Space 7
4 marks · HardA closed cone has a base radius of 6 cm and a perpendicular height of 8 cm.
Calculate the slant height of the cone. Give your answer to 3 significant figures.
Calculate the total surface area of the cone. Give your answer to 3 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 10 cm
(b) 302 cm^2
Common mistakes: using height instead of slant height for curved surface; omitting base area
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Applies Pythagoras' theorem: l = sqrt(r² + h²).
M2 (b) · 1 mark · Curved surface area: uses πrl with correct l from (a). (follow-through)
M3 (b) · 1 mark · Adds base area (πr²) to total surface area. (follow-through)
A1 (b) · 1 mark · Correct total surface area to 3 significant figures: 302 cm². (follow-through)
Worked solution
a) Slant height l = √(r² + h²)
b) Curved surface area = πrl = π × 6 × 10 = 60π ≈ 188 cm²
Base area = πr² = π × 6² = 36π ≈ 113 cm²
Total surface area = 188 + 113 = 301 cm² (to 3 s.f., 302 cm²)