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Chapter 8: Q34. (page 415)

A circle has a radius with endpoints at $(2, 5)$ and $(- 1, - 4)$ . Find the circumference and area of the circle.

Short Answer

Expert verified

The circumference and area of the circle are59.6 unitsand282.9 square units respectively.

Step by step solution

01

Step 1. Given Information.

Given a circle has a radius with endpoints $(2, 5)$ and $(- 1, - 4)$ .

The circumference and area of the circle are to be determined.

02

Step 2. Explanation.

The distance between two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ is given by $d = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}}$ .

Plugging the given values in the equation to find the radius:

\begin{array}{l} r = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ r = \sqrt{{(鈭� 1 鈭� 2)}^{2} + {(鈭� 4 鈭� 5)}^{2}} \\ r = \sqrt{{(鈭� 3)}^{2} + {(鈭� 9)}^{2}} \\ r = \sqrt{9 + 81} \\ r = \sqrt{90} \\ r = 3 \sqrt{10} \end{array}

The circumference of a circle with radius r is given by $C = 2 蟺 r$

Plugging the values in the equation:

\begin{array}{l} C = 2 蟺 r \\ C = 2 脳 \frac{22}{7} 脳 3 \sqrt{10} \\ C = 59.6 units \end{array}

The area of a circle with radius r is given by $A = 蟺 r^{2}$

Plugging the values in the equation:

\begin{array}{l} A = 蟺 r^{2} \\ A = \frac{22}{7} {(3 \sqrt{10})}^{2} \\ A = \frac{22}{7} (90) \\ A = 282.9 squareunits \end{array}

03

Step 3. Conclusion.

Hence, the circumference and area of the circle are 59.6 units and 282.9 square units respectively.

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