Find the area of the axial section of the cone if its generatrix is 5 cm and the radius of the base is 3 cm.
| September 20, 2021 | education
1. By the condition of the problem, it is known that the generatrix of the cone is 5 cm, and the radius of the base is 3 cm.
2. The area S of the axial section of the cone, which is an isosceles triangle, will be calculated by the formula
S treug = 1/2 * base length * height.
The length of the base is 2 * radius = 2 * 3 cm = 6 cm.
The height h is determined by the Pythagorean theorem from a right-angled triangle with a leg of 3 cm and a hypotenuse of 5 cm
h² = 5² – 3² = 9, whence h = √16 = 4 cm.
S = 1/2 * 6 cm * 4 cm = 12 cm².
Answer: The axial cross-sectional area is 12 cm².
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