Question

A sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.

What is the radius of the golf ball?
If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, how can the radius vary?
identify epsilon and limit

Answer 1

Given that the sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.

The golf ball is of spherical shape and the volume of a sphere is given by

`V= (4)/(3) \pi r^3`

The radius of the golf ball is given by

`(4)/(3) \pi r^3=2.48 \\ \\ \Rightarrow r^3= (3*2.48)/(4\pi) =0.592 \\ \\ \Rightarrow r= \sqrt[3]{0.592} =0.84 cm`

For V = 2.45

`(4)/(3) \pi r^3=2.45 \\ \\ \Rightarrow r^3= (3*2.45)/(4\pi) =0.585 \\ \\ \Rightarrow r= \sqrt[3]{0.585} =0.8363 cm`

For V = 2.51

`(4)/(3) \pi r^3=2.51 \\ \\ \Rightarrow r^3= (3*2.51)/(4\pi) =0.599 \\ \\ \Rightarrow r= \sqrt[3]{0.599} =0.8431 cm`

Thus, If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, then the radius can vary between 0.8363 and 0.8431.


`\lim_(r \to 0.84) V(r) =2.48`
because

`|V(r)-2.48|\ \textless \ 0.03`
whenever

`0\ \textless \ |r-0.84|\ \textless \ 0.0034`