Answer to Question #148835 in Geometry for anlp

Question

If a sphere is inscribed in a cube of side What is the volume of the sphere?

Answer 1

If the sphere is inscribed in a cube of side $a$ , then its diameter is $d=a.$

Then the radius of the sphere is $r=\dfrac{d}{2}=\dfrac{a}{2}.$

 The volume of the sphere is

$$V=\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\pi (\dfrac{a}{2})^3$$

$$=\dfrac{\pi a^3}{6} (units^3)$$

$V=\dfrac{\pi a^3}{6} cubic \ units$