Chapter 6.6, Problem 41PPS

To determine

The area of the circle having radius equal to $3x^{\frac{2}{3}}{y}^{\frac{1}{5}}{z}^2$ .

Answer to Problem 41PPS

The area of the circle is $9\pi x^{\frac{4}{3}}{y}^{\frac{2}{5}}{z}^4\text{ sq}\text{. units}$ .

Explanation of Solution

Given information: The radius $\left(r\right)$ of the circle is $3x^{\frac{2}{3}}{y}^{\frac{1}{5}}{z}^2$ .

Formula used: The area of circle is given by the formula,

  $\text{Area of circle}=\pi r^2\mathrm{....}\left(\text{where}\left(r\right)\text{is radius}\right)$

Calculation: Plugging for radius $\left(r\right)$ equal to $3x^{\frac{2}{3}}{y}^{\frac{1}{5}}{z}^2$ in the formula for area of circle.

  $\begin{array}{c}\text{Area of circle}=\pi {\left(3x^{\frac{2}{3}}{y}^{\frac{1}{5}}{z}^2\right)}^2\\ =9\pi {\left(x^{\frac{2}{3}}\right)}^2{\left(y^{\frac{1}{5}}\right)}^2{\left(z^2\right)}^2\\ =9\pi x^{\frac{4}{3}}{y}^{\frac{2}{5}}{z}^4\text{ sq}\text{. units}\end{array}$