The height of the cylinder is 12 cm greater than its radius, and the total surface area is 288п cm2.

| January 10, 2021 | education

The height of the cylinder is 12 cm greater than its radius, and the total surface area is 288п cm2. Find the radius of the base and the height of the cylinder.

Let the radius of the circle at the base of the cylinder be X cm, then, according to the condition, the height of the cylinder is (X + 12) cm.
The base area of the cylinder will be equal to: Sbn = n * X ^ 2 cm2.
The area of the lateral surface of the cylinder will be equal to: Side = 2 * n * X * (X +12) cm.
Then S side + 2 * Sosn = 288 * p.
2 * n * X * (X +12) + 2 * n * X ^ 2 = 288 * n.
X * (X + 12) + X ^ 2 = 144.
2 * X2 + 12 * X = 144.
X2 + 6 * X – 72 = 0.
Let’s solve the quadratic equation.
X = R = 6 cm.
H = OO1 = 6 + 12 = 18 cm.
Answer: The base radius is 6 cm, the height is 18 cm.



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