Chapter 11.8, Problem 32HP

To determine

To calculate: The radius and areaof the circle such that its area lie between 800 square centimeters and 820 square centimeters.

Answer to Problem 32HP

The radius of the circle is 16 centimetersand area of the circle is $804.28$square centimeters.

Explanation of Solution

Given information:

The area of the circle must lie between 800 square centimeters and 820 square centimeters.

Formula used:

The area A of a circle with radius r is $\pi r^2$ square units.

Calculation:

Consider the provided statement that area of the circle must lie between 800 square centimeters and 820 square centimeters.

Construct a circle with radius as 16 centimeters.

  

Recall that area A of a circle with radius r is $\pi r^2$ square units.

Therefore, area A of a circle with radius as 16 centimeters is,

  $\begin{array}{c}A=\pi \times {\left(16\text{ cm}\right)}^2\\ \text{=804}{\text{.247719 cm}}^2\end{array}$

Round off the result obtained to nearest tenth,

  $\begin{array}{c}A=\pi \times {\left(16\text{ cm}\right)}^2\\ \text{=804}{\text{.247719 cm}}^2\\ \approx \text{804}{\text{.28 cm}}^2\end{array}$

Thus, the radius of the circle is 16 centimeters and area of the circle is $804.28$ square centimeters.