Chapter 11.6, Problem 1PSA

a

To determine

To calculate: The area and circumference of circle with radius 1.

Answer to Problem 1PSA

The area and circumference of circle is $3.14$

  ${\text{units}}^2$ and $6.28$ units respectively.

Explanation of Solution

Given information :

Radius of circle is $(r)=1$ .

Formula used: Area of circle = $\pi r^2$ ,

Circumference of circle = $2\pi r$

Calculation: Area of circle = $\pi r^2$

  $\begin{array}{l}$ \Rightarrow \frac{22}{7}\times {(1)}^2$\Rightarrow \frac{22}{7}\times 1\\ \Rightarrow \frac{22}{7}\\ \Rightarrow 3.14\end{array}$

Now, Circumference of circle = $2\pi r$

  $\begin{array}{l}\Rightarrow 2\times \frac{22}{7}\times 1\\ \Rightarrow \frac{44}{7}\\ \Rightarrow 6.28\end{array}$

b

To determine

To calculate: The area and circumference of circle whose radius is 8.

Answer to Problem 1PSA

The area and circumference of circle is $201.14{\text{ units}}^2$ units and $50.28\text{ units}$ respectively.

Explanation of Solution

Given information :

Radius of circle is $(r)=8$ .

Formula used: Area of circle = $\pi r^2$

Circumference of circle = $2\pi r$

Calculation: Area of circle = $\pi r^2$

  $\begin{array}{l}$ \Rightarrow \frac{22}{7}\times {(8)}^2$\Rightarrow \frac{22}{7}\times 64\\ \Rightarrow \frac{1408}{7}\\ \Rightarrow 201.14\end{array}$

Now, Circumference of circle = $2\pi r$

  $\begin{array}{l}\Rightarrow 2\times \frac{22}{7}\times 8\\ \Rightarrow \frac{352}{7}\\ \Rightarrow 50.28\end{array}$

c

To determine

To calculate: The area and circumference of circle whose radius is 15.

Answer to Problem 1PSA

The area and circumference of circle is $707.14{\text{ units}}^2$ and $94.28$ units respectively.

Explanation of Solution

Given information :

Radius of circle is $(r)=15$ .

Formula used: Area of circle = $\pi r^2$

Circumference of circle = $2\pi r$

Calculation: Area of circle = $\pi r^2$

  $\begin{array}{l}$ \Rightarrow \frac{22}{7}\times {(15)}^2$\Rightarrow \frac{22}{7}\times 225\\ \Rightarrow \frac{4950}{7}\\ \Rightarrow 707.14\end{array}$

Now, Circumference of circle = $2\pi r$

  $\begin{array}{l}\Rightarrow 2\times \frac{22}{7}\times 15\\ \Rightarrow \frac{660}{7}\\ \Rightarrow 94.28\end{array}$