For the accompanying right circular cone, h=5 m and r=3 m.
Find the exact slant height (in meters).
√(h² + r²) = √(5² + 3²) = √34 m
a) Lateral area (in square meters)
exact: πr√(h² + r²) = π(3)√34 ≈ 43.47 m²
approximate: 43.47 m²
base area (in square meters)
exact: πr² = π(3)² = 9π ≈ 28.27 m²
approximate: 28.27 m²
b) Total area (in square meters)
exact: πr(r + √(h² + r²)) = π(3)(3 + √34) ≈ 71.74 m²
approximate: 71.74 m²
c) Volume (in cubic meters)
exact: (1/3)πr²h = (1/3)π(3)²(5) = 15π ≈ 47.12 m³
approximate: 47.12 m³