Question

Найдите площадь поверхности цилиндра с радиусом 3 см, а образующая 9 см.

Answer 1

Sповерх равна = 2(Пr^2)+ l*2Пr, где l - образующая. S= 18П + 54П=72П

Answer 2

Calculation of the Surface Area of a Cylinder

To find the surface area of a cylinder, we can use the formula:

S = 2πrh + 2πr^2

where: - S is the surface area of the cylinder - π is a mathematical constant approximately equal to 3.14 - r is the radius of the cylinder's base - h is the height or length of the cylinder

In this case, the radius of the cylinder is given as 3 cm, and the height or length (also known as the generatrix) is given as 9 cm.

Substituting these values into the formula, we have:

S = 2π(3 cm)(9 cm) + 2π(3 cm)^2

Simplifying the equation, we get:

S = 2π(27 cm^2) + 2π(9 cm^2)

S = 54π cm^2 + 18π cm^2

Combining like terms, we have:

S = 72π cm^2

Now, let's calculate the numerical value of the surface area.

Using the value of π as approximately 3.14, we can substitute it into the equation:

S ≈ 72(3.14) cm^2

Calculating the result, we find:

S ≈ 226.08 cm^2

Therefore, the surface area of the cylinder with a radius of 3 cm and a generatrix of 9 cm is approximately 226.08 cm^2.