Chapter 8.4, Problem 34MCQ

a.

To determine

To write the expression for the area of the largest disc.

Answer to Problem 34MCQ

  $\pi \left(x^2+6.5x+10.5625\right)$ and $3.14\left(x^2+6.5x+10.5625\right)$ .

Explanation of Solution

Given:

Radius of the largest disc $=\left(x+3.25\right)$ inches

Formula used:

Square Formula:

  ${\left(a\pm b\right)}^2=a^2\pm 2ab+b^2$

Area of disc $=\pi r^2$

Calculation:

Given, radius of the largest disc $=\left(x+3.25\right)$ inches.

Now,

Area of the largest disc $=\pi r^2$

  $\begin{array}{l}=\pi {\left(x+3.25\right)}^2\\ =\pi \left(x^2+2\times \left(x\right)\times \left(3.25\right)+{\left(3.25\right)}^2\right)\\ =\pi \left(x^2+6.5x+10.5625\right)\end{array}$       [ $\because {\left(a\pm b\right)}^2=a^2\pm 2ab+b^2$ ]

It can also be written as:

Area of the largest disc $=\pi \left(x^2+6.5x+10.5625\right)$

  $=3.14\left(x^2+6.5x+10.5625\right)$

Conclusion:

Therefore, area of the largest disc in two different expressions is $\pi \left(x^2+6.5x+10.5625\right)$ and $3.14\left(x^2+6.5x+10.5625\right)$ .