The length of the generatrix of the truncated cone is 13cm, the height is 12cm.

| January 3, 2021 | education

The length of the generatrix of the truncated cone is 13cm, the height is 12cm. Find the radii of the bases if the perimeter of the axial section of the truncated cone is 56 cm.

From the right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the leg AН.
AH2 = AB2 – BH2 = 132 – 122 = 169 – 144 = 25.
AH = 5 cm.
Let’s draw the height of the SC. The axial section of the truncated cone is an isosceles trapezoid of AВСD, then the segment DK = AH = 5 cm, СD = AB = 13 cm.
Quadrangle ВСKS rectangle, then BC = НK. Let BC = НK = X cm.
Then AD = AH + НK + DK = 5 + X + 5 = 10 + X cm.
The section perimeter is equal to: Ravsd = AB + BC + СD + AD = 56 cm.
13 + X + 13 + 10 + X = 56.
2 * X = 56 – 36 = 20.
X = BC = 20/2 = 10 cm.
Then BO1 = BC / 2 = 10/2 = 5 cm.
BP = 10 + 10 = 20 cm.
AO = AD/ 2 = 20 / = 10 cm.
Answer: The radii of the bases are 5 cm and 10 cm.



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