Find the area of the axial section of the truncated cone, if the height is truncated.
| April 25, 2021 | education
Find the area of the axial section of the truncated cone, if the height is truncated. The cone is 10 cm, and the radius of its bases is 5 cm and 7 cm.
If the radii of the bases of the truncated cone are 5 cm and 7 cm, then the diameters of these bases are 10 cm and 14 cm, respectively.
The axial section of the truncated cone is an isosceles trapezoid, the bases of which are equal to the diameters of the bases of the truncated cone. Consequently, the area of the axial section of this truncated cone is equal to the area of a trapezoid with bases of 10 cm and 14 cm and a height of 10 cm.
The area of a trapezoid is defined as the product of the half-sum of the bases and the height:
Ssection = 10 * (10 + 14) / 2 = 10 * 24/2 = 10 * 12 = 120 cm2.
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