Find the height and radius of the cylinder if the lateral area is 30 cm2 and the entire area is 50 cm2.

univerkov | September 17, 2021 | education

Let us designate the area of the lateral surface of the cylinder SБП = 30 cm2, the area of the entire surface is simply S = 50 cm2. It is necessary to calculate the radius of the base R and the height of the cylinder H.

First, we find the area of one base Sо.

Since the total area is the sum of the lateral surface area and two base areas, we can write down the formula.

S = SBP + 2Sо.

Then Sо = (S – SBP) / 2.

Substitute the values and calculate.

Sо = (50 – 30) / 2.

Sо = 10 cm2.

Knowing that Sо = nR2, and SBP = 2пRH, we can calculate the radius and height.

1) R = √ (Sо / п).

R = √ (10 / 3.14).

R ≈ 1.78 cm.

2) H = SBP / (2pR).

H = 30 / (2 * 3.14 * 1.78).

H ≈ 2.68 cm.

Answer: The height of the cylinder is approximately 2.68 cm, the radius is approximately 1.78 cm.

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