Question

The area of a circle is 676π square centimeters. Find the diameter.

Solution

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We know that the area of the circle is given by the formula:

Area of a Circle=πradius2\begin{aligned} \text{Area of a Circle}&=\pi\cdot \text{radius}^2 \end{aligned}

we now find radius as below:

Area of a Circle=πradius2676π centimeters2=πradius2radius=676π centimeters2π=676 centimeters2=676 centimeters=26 centimeters\begin{aligned} \text{Area of a Circle}&=\pi\cdot \text{radius}^2\\ 676\pi\text{ centimeters}^2&=\pi\cdot \text{radius}^2\\ ⇒\text{radius}&=\sqrt{\frac{676\pi\text{ centimeters}^2}{\pi}}\\ &=\sqrt{676\text{ centimeters}^2}\\ &=\sqrt{676}\text{ centimeters}\\ &=26\text{ centimeters} \end{aligned}

Note that we disregard the negative radius since radius must be non-negative.

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