A Special Spherical Ball

Geometry Level 1

I have a magical machine that can scan a 3D object and determine whether the numerical value (in units) of its surface area is equal to the numerical value (in units) of its volume. After experimenting with different objects in my lab, the only thing that the machine gives an output of is my spherical ball.

What is the radius of my spherical ball (in units)?

3 6 9 12

1 solution

Aaron Tsai
May 16, 2016

Suppose the sphere has radius $r$ . Setting the equation for the volume of a sphere equal to the equation for the surface area of a sphere, we have:

$\dfrac{4}{3}\pi r^3=4\pi r^2$

$\dfrac{r^3}{3}=r^2$

$r=3$

The radius of the sphere is $\boxed{3}$ units.

Yes, we just need to know the formula for the surface area and the volume of the sphere. Thank you for your solution!

Chung Kevin - 5 years ago

A Special Spherical Ball

1 solution

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