Chapter 6.1, Problem 14E

(a)

To determine

The error value

Answer to Problem 14E

The error value decreases as the value of n gets increases.

Explanation of Solution

Given information:

Use a geometry formula to find the volume V of the sphere

Formula used:

  $V=\frac{4}{3}\pi r^3$

Calculation:

Since, volume of sphere is given by

  $V=\frac{4}{3}\pi r^3$

Here,

  $r=5$

So

  $\begin{array}{l}V=\frac{4}{3}\pi {\left(5\right)}^3\\ V=523.59878\end{array}$

Now calculate the error for each value of n. Subtract this value from each volume being obtained.

  

Conclusion:

The error value decreases as the value of n gets increases.

(b)

To determine

The percentage error is determined by using the MRAM approximation.

Answer to Problem 14E

The percentage of error decreases as the n value increases.

Explanation of Solution

Given information:

Use a geometry formula to find the volume V of the sphere

Formula used:

On multiplying the error by 100 then divide by volume.

Calculation:

Now from percentage error, multiply the error by 100 then divide by volume Obtained for each value of n.

  

Conclusion:

The percentage of error decreases as the n value increases.