A hole of a radius of 1cm is pierced in a sphere of a 4cm radius. Calculate the volume of the remaining sphere.

I know that the volume of a sphere with an exterior radius is of:

V = pie(R^2 - r^2) dH

where R^2 is the exterior surface area and r^2 is the interior surface area. dH is the thickness.

How would I go about finding the thickness? And for R and r, do I simply just plug in the values that are given to me?

Thank you.

To find the thickness (dH) of the remaining sphere, you need to subtract the radius of the hole (r) from the radius of the original sphere (R). So in this case, the thickness would be:

dH = R - r
= 4 cm - 1 cm
= 3 cm

As for the values of R and r, yes, you would plug in the given values. In this case, R is 4 cm because it's the radius of the original sphere, and r is 1 cm because it's the radius of the hole. Substituting these values into the volume equation, you can then calculate the volume of the remaining sphere.