Question

Шар получен вращением полукруга площадью 8п вокруг диаметра. Найти объем шара

Answer 1

Sкруга=πR²
Sкруга/2=πR²/2
8π=πR²/2
R²=16
R=4
V=(4/3)πR³
V=(4/3)π*4³
V=256π/3

Answer 2

Calculation of the Volume of a Sphere

To find the volume of a sphere, we need to know the radius or diameter of the sphere. In this case, we are given that the sphere is obtained by rotating a semicircle with an area of 8π around its diameter.

Let's break down the problem step by step:

1. Find the radius of the sphere: - The area of a semicircle is given by the formula A = (πr^2)/2, where A is the area and r is the radius. - In this case, the area of the semicircle is 8π, so we can set up the equation (πr^2)/2 = 8π. - Simplifying the equation, we get πr^2 = 16π. - Dividing both sides of the equation by π, we find that r^2 = 16. - Taking the square root of both sides, we find that r = 4.

2. Calculate the volume of the sphere: - The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius. - Substituting the value of r we found earlier, we get V = (4/3)π(4^3). - Simplifying the equation, we get V = (4/3)π(64). - Multiplying, we find that V = (256/3)π.

Therefore, the volume of the sphere obtained by rotating a semicircle with an area of 8π around its diameter is (256/3)π cubic units.

Please note that the above calculations are based on the given information and assumptions. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.

Code to Calculate the Volume of a Sphere

If you would like to calculate the volume of a sphere using code, here's an example in Python:

import math

def calculate_sphere_volume(radius):
    volume = (4/3) * math.pi * radius**3
    return volume

# Example usage:
radius = 4
volume = calculate_sphere_volume(radius)
print("The volume of the sphere is:", volume)

In the code above, we define a function `calculate_sphere_volume` that takes the radius of the sphere as input and returns the volume. We then use this function to calculate the volume of a sphere with a radius of 4 and print the result.