Question

Объём шара равен 36п см3. Найдите площадь сферы, ограничивающей данный шар

Answer 1

V=4/3pi R³
R³=V*3/4 pi
R=∛36 pi *3/4 pi=∛27=3
S=4pi R²
S=4pi 3²=36 pi

Answer 2

Calculation of Sphere Surface Area

To find the surface area of a sphere that encloses a given sphere with a volume of 36 cm³, we can use the formula for the surface area of a sphere:

Surface Area (S) = 4πr²

where: - S is the surface area of the sphere, - π is a mathematical constant approximately equal to 3.14159, - and r is the radius of the sphere.

To find the radius of the sphere, we can use the formula for the volume of a sphere:

Volume (V) = (4/3)πr³

Given that the volume of the sphere is 36 cm³, we can rearrange the formula to solve for the radius:

r = (3V / 4π)^(1/3)

Let's calculate the radius and then use it to find the surface area of the sphere.

Calculation Steps:

1. Calculate the radius using the formula: r = (3V / 4π)^(1/3) 2. Substitute the given volume: V = 36 cm³ 3. Calculate the radius: r = (3 * 36 / (4 * π))^(1/3) 4. Simplify the expression: r = (108 / (4 * π))^(1/3) 5. Calculate the approximate value of the radius using the value of π: r ≈ 1.732 cm 6. Substitute the radius into the formula for surface area: S = 4πr² 7. Calculate the surface area: S = 4 * π * (1.732)^2

Let's calculate the surface area of the sphere.

Calculation:

1. Calculate the radius: - r = (108 / (4 * π))^(1/3) - r ≈ 1.732 cm

2. Calculate the surface area: - S = 4 * π * (1.732)^2 - S ≈ 37.69 cm²

Therefore, the surface area of the sphere that encloses the given sphere with a volume of 36 cm³ is approximately 37.69 cm².