Question

Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2

Answer 1

The volume of the sphere is
`V=288\pi\ m^3`

Explanation:

The question in English is

Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2

we know that

The radius of the maximum circle in the sphere is equal to the radius of the sphere

Step 1

Find the radius of the maximum circle

The area of the circle is

`A=\pi r^(2)`

we have

`A=36\pi\ m^2`

substitute and solve for r

`36\pi=\pi r^(2)`

Simplify

`36=r^(2)`

take the square root both sides

`r=6\ m`

Step 2

Find the volume of the sphere

The volume of the sphere is

`V=(4)/(3)\pi r^(3)`

substitute the value of r

`V=(4)/(3)\pi (6)^(3)`

`V=288\pi\ m^3`