Question

Площадь поверхности шара равна 225Пм2.Надите объем шара

Answer 1

V =(4/3)*π*R³ ;
4πR² =225π м² ⇒R =15/2 м.
V =(4/3)*π*R³ =(4/3)* π*(15/2 м)³ =562,5π м³ .

Answer 2

Calculating the Volume of a Sphere

To find the volume of a sphere when the surface area is given, we can use the formula:

V = (4/3) * π * r^3

Where: - V = volume of the sphere - π (pi) is a constant approximately equal to 3.14159 - r = radius of the sphere

Calculating the Radius of the Sphere

First, we need to calculate the radius of the sphere using the given surface area.

Given: Surface area of the sphere = 225π m^2

We can use the formula for the surface area of a sphere to find the radius: A = 4 * π * r^2

Where: - A = surface area of the sphere - π (pi) is a constant approximately equal to 3.14159 - r = radius of the sphere

Solving for the Radius

Rearranging the formula to solve for the radius (r): r = √(A / (4 * π))

Substituting the given surface area: r = √(225π / (4 * π))

Solving for r: r = √(225 / 4) r = √56.25 r = 7.5 meters

Calculating the Volume

Now that we have the radius, we can calculate the volume of the sphere using the formula: V = (4/3) * π * r^3

Substituting the radius: V = (4/3) * π * (7.5)^3 V ≈ 1767.15 cubic meters

Therefore, the volume of the sphere is approximately 1767.15 cubic meters.