Chapter 6.1, Problem 25E

To determine

To find: The volume of Nose Cone.

Answer to Problem 25E

The volume of Nose Cone is $39.2699$ .

Explanation of Solution

Given information :

Volume of cylinder is given by-

  $V=\pi r^{2}h$

Here,

  $r=\sqrt{x}$

  $h=\text{Δ}x$

Calculation :

Use MRAM with

  $\begin{array}{cc}f(x)& =\pi {(\sqrt{x})}^2\\ & =\pi (x)\end{array}$

And interval [0, 5] which is partitioned into five equal subintervals so, length of a subinterval is 1.0. So, substitutes the value of $\text{x}$ with 1.0 difference in $\text{f}(\text{x})$ from $0.5,1.5\dots .$ up to 4.5 and then add and multiply with 1.0 then it is equal to S.

  $\begin{array}{cc}S& =\pi [0.5+1.5+2.5+3.5+4.5]\\ & \approx 39.2699\end{array}$