Question

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

Answer 1

Answer:

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

Step-by-step 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

$V=\frac{4}{3}\pi r^{3}$

substitute the value of r

$V=\frac{4}{3}\pi (6)^{3}$

$V=288\pi\ m^3$