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Find the diameter of a circle with an area of 415.48 square inches.

Find the diameter of a circle with an area of $415$ . $48$ square inches.

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Solve proportions: word problems

Full solution

Q. Find the diameter of a circle with an area of

415

.

48

square inches.

Recall formula for area: Recall the formula for the area of a circle, which is $A = \pi r^2$ , where $A$ is the area and $r$ is the radius of the circle.
Given area and solve for radius: We are given the area $A = 415.48$ square inches. We need to solve for the radius $r$ first before we can find the diameter.
Rearrange formula to find radius: Rearrange the area formula to solve for $r$ . This gives us $r^2 = \frac{A}{\pi}$ . We will then take the square root of both sides to solve for $r$ .
Substitute area into formula: Substitute the given area into the rearranged formula: $r^2 = \frac{415.48}{\pi}.$
Calculate radius: Calculate $r^2$ using a calculator: r^2 = rac{415.48}{ ext{ extpi}} hickapprox 132.25.
Find diameter formula: Take the square root of both sides to find the radius: $r \approx \sqrt{132.25} \approx 11.5$ inches.
Substitute radius into diameter formula: Recall that the diameter $d$ of a circle is twice the radius: $d = 2r$ .
Calculate diameter: Substitute the radius into the formula for diameter: $d = 2 \times 11.5$ inches.
Calculate diameter: Substitute the radius into the formula for diameter: $d = 2 \times 11.5$ inches.Calculate the diameter: $d = 23$ inches.

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