In a straight cylinder, the base radius is 3 cm, the lateral surface area is equal to two base areas. Find the height.

In order to calculate the height of the cylinder, we use the formula for the area of the lateral surface of the cylinder:

Sb.p. = 2πRH;

H = Sb.p. / (2πR), where:

Sb.p. – lateral surface area;

H – height;

R is the radius of the base;

π – number ≈ 3.14.

Since the area of the lateral surface of the cylinder is equal to two areas of the bases

Sb.p. = 2 Sos.,

find the area of the base of the cylinder:

Sos. = πR ^ 2;

Sos. = 3.14 * 3 ^ 2 = 3.14 * 9 = 28.26 cm2;

Sb.p. = 2 * 28.26 = 56.52 cm2;

H = 56.52 / (2 * 3.14 * 3) = 56.52 / 18.84 = 3 cm.

Answer: The height of the cylinder is 3 cm.