Chapter 12.6, Problem 39PPS

a.

To determine

Calculate the volume of the portion of the sphere that represent orange production in California.

Answer to Problem 39PPS

The volume of the portion is $268c{m}^3$ .

Explanation of Solution

Given:

It is given in the question that the radius of the sphere is $4cm$ and the figure is shown below:

  

Concept Used:

In this, use the concept of volume of sphere i.e. $V=\frac{4}{3}\pi r^3$ .

Calculation: Here, $r=4cm$ .

  $\begin{array}{l}V=\frac{4}{3}\pi r^3\\ $ V=\frac{4}{3}\pi {(4)}^3$V=\frac{4}{3}\pi (64)\\ V=\frac{803.9}{3}=268c{m}^3\end{array}$

Conclusion:

The volume is $268c{m}^3$ .

b.

To determine

Calculate the surface area of the portion of the sphere that represent orange production in Florida.

Answer to Problem 39PPS

The surface area of the portion is $162.81c{m}^2$ .

Explanation of Solution

Given:

It is given in the question that the radius of the sphere is $4cm$ and the figure is shown below:

  

Concept Used:

In this, use the concept of surface area of a sphere i.e. $S=4\pi r^2$ .

Calculation: Here, $r=4cm$ .

  $S=4\pi r^2=4\pi {(4)}^2=64\pi =201c{m}^2$

Now, the surface of the Florida i.e. $81\%$ = $=201\cdot 81\%=201\cdot 0.81=162.81c{m}^2$

Conclusion:

The surface area is $162.81c{m}^2$ .