The radius of the base of the cylinder is R; the lateral surface is equal to the sum of the areas of the bases.

| September 24, 2021 | education

The radius of the base of the cylinder is R; the lateral surface is equal to the sum of the areas of the bases. Find the height.

1. The area of ​​the lateral surface of the cylinder is found by the formula:
S side. = 2πRH,
where R is the radius of the base, H is the height of the cylinder.
2. At the base of the cylinder lies a circle, then the area of ​​the base of the cylinder is found by the formula for finding the area of ​​a circle:
Sosn. = πR².
3. By condition, the area of ​​the lateral surface of the cylinder is equal to the sum of the areas of the bases. The cylinder has two equal bases, then:
S side. = Sosn. + S main;
S side. = 2Sn.
Substitute the area values ​​into equality:
2πRH = 2πR².
Let’s express H in proportion:
H = 2πR² / 2πR (2πR in the numerator and 2πR in the denominator cancel out);
H = R.
Answer: H = R.



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