a cone has a radius of 6cm and height 9 calculate a)the volume and curved surface area b) total surface area
1 answer:
Answer:
V = 339.3 cm³; L = 203.9 cm²; A = 317.0 cm²
Step-by-step explanation:
a) Volume
The formula for the volume (V) of a cone is
V = ⅓πr²h
V = ⅓π × 6² × 9
V = ⅓π × 36 × 9
V = 108π cm³
V ≈ 339.3 cm³
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Curved surface area
The formula for the lateral surface area (L) of a cone is
L = πr√(r² + h²)
L = π×6√(36 + 81)
L = 6π√[9(4 + 9)]
L = 6π√(9 × 13)
L = 18π√13 cm²
L ≈ 203.9 cm²
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b) Base surface area
The base is a circle, so the formula for base surface area (B) is
B = πr²
B = π×6²
B = 36π cm²
B ≈ 113.1 cm²
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Total surface area
A = L + B
A = 18π√(13 +36π)
A = 18π(2 + √13) cm²
A ≈ 203.9 + 113.1
A ≈ 317.0 cm²
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