Question

Найти объем шара, вписанного в куб. Площадь поверхности куба равна 72 см в квадрате

Answer 1

площадь поверхности куба=6*a*a (a-сторона куба) .отсюда сторона куба равна 2*(корень из 3).радиус шара вписанного в куб равен половине стороны куба.половине а и равен = корень из 3.объем шара =4/3*п*r в кубе и равен 4/3*п*(корень из 3 )

Answer 2

Finding the Volume of a Sphere Inscribed in a Cube

To find the volume of a sphere inscribed in a cube, we can use the formula for the volume of a sphere and the given information about the cube's surface area.

The formula for the volume of a sphere is given by:

V = (4/3)πr³

Where: - V = volume of the sphere - π ≈ 3.14159 - r = radius of the sphere

Given that the surface area of the cube is 72 cm², we can use this information to find the radius of the inscribed sphere.

Calculating the Radius of the Inscribed Sphere

The surface area of a cube is given by the formula:

A = 6s²

Where: - A = surface area of the cube - s = length of a side of the cube

Given that the surface area of the cube is 72 cm², we can solve for the length of a side of the cube:

72 = 6s²

Solving for s:

s² = 12

s = √12

Calculating the Volume of the Inscribed Sphere

Now that we have the length of a side of the cube, we can find the radius of the inscribed sphere, which is half the length of a side of the cube.

r = s/2

Substituting the value of s:

r = √12 / 2

Now, we can use the formula for the volume of a sphere to find the volume of the inscribed sphere.

V = (4/3)π(√12 / 2)³

Calculating the volume:

V ≈ 4.18879 cm³

So, the volume of the sphere inscribed in the cube is approximately 4.18879 cubic centimeters.