Question

Find the approximately the difference between the areas of two spheres whose radii are 4 feet and 4.05 feet.

Answer 1

We have $r_1=4ft$ and $r_2=4.05ft$

And total surface area of a sphere is

$$S=4\pi r^2$$

,where $r$ is the radius of the sphere.

So, difference between the two surface areas:-

$$S_2-S_1\\ =4\pi r_2^2-4\pi r_1^2\\ =4\pi(r_2^2-r_1^2)\\ =4\pi((4.05)^2-(4)^2)\\ =4\pi(16.4025-16)\\ =4\pi(0.4025)\\ =4\cdot3.14\cdot0.4025\\ =5.0554\>sq\>ft$$

So, the difference between the surface areas is $5.0554$ sq ft.