Question

Объем цилиндра 96п см^3, площадь его осевого сечения - 48 см^2 найдите площадь сферы, описанной около цилиндр.

Answer 1

Объём цилиндра 96π см³, площадь его осевого сечения - 48 см². Найдите площадь сферы, описанной около цилиндра.

Answer 2

Calculation of Cylinder Volume and Cross-Sectional Area

To find the surface area of the sphere circumscribing the cylinder, we first need to calculate the volume and cross-sectional area of the cylinder.

Given: - Volume of the cylinder: 96 cm³ - Cross-sectional area of the cylinder: 48 cm²

Let's calculate the height (h) and radius (r) of the cylinder using the given information.

The volume (V) of a cylinder is given by the formula: V = πr²h From the given volume, we have: 96 cm³ = πr²h

The cross-sectional area (A) of a cylinder is given by the formula: A = πr² From the given cross-sectional area, we have: 48 cm² = πr²

Now, let's solve these equations to find the values of r and h.

Dividing the equation for volume by the equation for cross-sectional area, we get: (96 cm³) / (48 cm²) = (πr²h) / (πr²)

Simplifying, we have: 2 cm = h

Substituting the value of h back into the equation for cross-sectional area, we can solve for r: 48 cm² = πr² r² = (48 cm²) / π r ≈ 3.08 cm

So, the height of the cylinder (h) is 2 cm and the radius (r) is approximately 3.08 cm.

Calculation of Sphere Surface Area

Now that we have the dimensions of the cylinder, we can calculate the surface area of the sphere circumscribing the cylinder.

The surface area (S) of a sphere is given by the formula: S = 4πr² Substituting the value of r, we can calculate the surface area of the sphere: S = 4π(3.08 cm)² S ≈ 118.08 cm²

Therefore, the surface area of the sphere circumscribing the given cylinder is approximately 118.08 cm².

Please note that the calculations provided are based on the given information and assumptions.

Answer 3

Для решения данной задачи необходимо использовать формулы для объема и площади цилиндра, а также формулу для площади сферы, описанной вокруг цилиндра.

Объем цилиндра вычисляется по формуле: V = π * r^2 * h, где V - объем цилиндра, π - число Пи, r - радиус основания цилиндра, h - высота цилиндра.

Площадь осевого