Question

Объём шара равен 36 пи см.найти площадь сферы ограничивающей этот шар

Answer 1

V=4/3πR³=36π
R³=27
R=3
S=4πR²=4π*9=36π

Answer 2

Calculation of Sphere's Surface Area

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

Surface Area of a Sphere = 4πr²

where 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 of a Sphere = (4/3)πr³

Given that the volume of the sphere is 36π cm³, we can set up the equation:

(4/3)πr³ = 36π

Simplifying the equation, we have:

r³ = (36π * 3) / 4

r³ = 27π

Taking the cube root of both sides, we find:

r = (27π)^(1/3)

Now that we have the radius, we can substitute it into the formula for the surface area of a sphere:

Surface Area of the Sphere = 4π * (27π)^(2/3)

Calculating the value, we get:

Surface Area of the Sphere ≈ 4π * 19.44 ≈ 77.76π cm².

Therefore, the surface area of the sphere that encloses the given sphere with a volume of 36π cm³ is approximately 77.76π cm².

Please note that the exact value of the surface area depends on the accuracy of the approximation of π used in the calculation.