Question

Высота цилиндра 6 дм, радиус основания 5 дм. найдите боковую поверхность и объем цилиндра

Answer 1

V=S*H=$\pi * r^{2} *h$=$\pi$*25*6=150$\pi$ дм^3
S(бок)=$2* \pi *r*h$=2*$\pi$*6=12$\pi$ дм

Answer 2

Calculation of the lateral surface area and volume of a cylinder

To find the lateral surface area and volume of a cylinder, we need to know the height and radius of the base. In this case, the height of the cylinder is 6 dm (decimeters) and the radius of the base is 5 dm.

Step 1: Calculate the lateral surface area (S) of the cylinder.

The formula for the lateral surface area of a cylinder is S = 2πrh, where r is the radius of the base and h is the height of the cylinder.

Substituting the given values, we have: r = 5 dm h = 6 dm

Using the formula, we can calculate the lateral surface area: S = 2πrh = 2π(5 dm)(6 dm) = 60π dm²

Therefore, the lateral surface area of the cylinder is 60π dm².

Step 2: Calculate the volume (V) of the cylinder.

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.

Substituting the given values, we have: r = 5 dm h = 6 dm

Using the formula, we can calculate the volume: V = πr²h = π(5 dm)²(6 dm) = 150π dm³

Therefore, the volume of the cylinder is 150π dm³.

To summarize: - The lateral surface area of the cylinder is 60π dm². - The volume of the cylinder is 150π dm³.

Please note that the values are given in terms of π, which represents the mathematical constant pi. If you need a numerical approximation, you can use the value 3.14 for π.

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