The circumference of a circle is 5π ft. What is the area, in square feet? Express your answer in terms of piπ.

Question

sxlvergxge · Answer

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surjithayer · Answer

$$circumference~of~circle=2\pi r$$
$$area~of~circle=\pi r^2$$

curriful · Answer

The circumference of a circle is given by the formula c=2 pi r, where r is the radius. In this problem, the circumference is given as 5pi ft. By rearranging the formula, we can find the radius, r=C/(2pi). Substituting the given value the radius is 5pi ft / (2pi) = 5/2 ft. The area of a circle is given by the formula A = pi r^2. Substituting the value of the radius, we get A = pi (5/2 ft)^2 = 25/4 pi ft^2. Therefore, the area of the circle is 25/4pi square feet.

curriful · Answer

@curriful wrote:

The circumference of a circle is given by the formula c=2 pi r, where r is the radius. In this problem, the circumference is given as 5pi ft. By rearranging the formula, we can find the radius, r=C/(2pi). Substituting the given value the radius is 5pi ft / (2pi) = 5/2 ft. The area of a circle is given by the formula A = pi r^2. Substituting the value of the radius, we get A = pi (5/2 ft)^2 = 25/4 pi ft^2. Therefore, the area of the circle is 25/4pi square feet.

i dont know if i did this right, is it right? -

surjithayer · Answer

$$2\pi r=5\pi ,r=\frac{ 5\pi }{ 2\pi}=\frac{ 5 }{ 2 }$$
$$area~A=\pi r^2=\pi(\frac{ 5 }{ 2 })^2=\frac{ 25 }{ 4}~sq.~ft.$$

curriful · Answer

@surjithayer wrote:

$$2\pi r=5\pi ,r=\frac{ 5\pi }{ 2\pi}=\frac{ 5 }{ 2 }$$ $$area~A=\pi r^2=\pi(\frac{ 5 }{ 2 })^2=\frac{ 25 }{ 4}~sq.~ft.$$

thanks for this, i wasnt sure if i was right or not -