The radii of the bases of the truncated cone are 10cm, 15cm, the generatrix is 30cm.
| February 24, 2021 | education
The radii of the bases of the truncated cone are 10cm, 15cm, the generatrix is 30cm. Find the total surface area of the truncated cone.
The total surface area of the truncated cone is equal to the sum of the lateral surface areas of the truncated cone and its bases. The bases of a truncated cone are circles and their area is calculated using the formula for the area of a circle:
S = π (r1 ^ 2 + (r1 + r2) l + r2 ^ 2), (r is the radius of rotation of the truncated cone; l is the generator of the truncated cone).
By condition, r1 = 10 cm, r2 = 15 cm, l = 30 cm.
Spp = pi * (R * l + r * l + R² + r²) = π * (15 * 30 + 10 * 30 + 15² + 10²) = π * (450 + 300 + 225 + 100) π = 1075p.
Answer. The total surface area of the truncated cone is 1075π cm2.
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