Question

Чему равен объем шара описанного около куба с ребром 4 см

Answer 1

1)Находим диагональ куба
   d=a√3, где а- ребро куба
   d=4√3см
2)Диаметр шара, описанного около куба равен диагонали этого куба
  D=d=4√3(см)
3)Радиус шара равен половине диаметра шара
   R=D/2=4√3/2=2√3(см)
4)Обём шара
  V=4πR³/3
  V=4π(2√3)³/3=4π*8*3√3 /3=32π√3/3 (см³)

Answer 2

Calculating the Volume of a Sphere Inscribed in a Cube

To find the volume of a sphere inscribed in a cube with a side length of 4 cm, we can use the formula for the volume of a sphere, which is given by:

V = (4/3)πr^3

Where: - V is the volume of the sphere - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the sphere

The radius of the sphere inscribed in the cube is half the length of the cube's side, which is 2 cm.

Calculation

Using the formula, we can calculate the volume of the sphere:

V = (4/3)π(2)^3

V = (4/3)π(8)

V = (32/3)π

Therefore, the volume of the sphere inscribed in the cube with a side length of 4 cm is (32/3)π cubic centimeters.