Question

Juan is clearing land in the shape of a circle to plant a new tree. The diameter of the space he needs to clear is 52 inches. By midday, he has cleared a sector of the land cut off by a central angle of 140 . What is the arc length and the area of land he has cleared by midday?

Answer 1

The central angle of 140 degrees illustrates the degree measure of the arc

The arc length cleared is 63.54 inches and the area of the land cleared is 826.00 square inches

How to determine the arc length

The given parameters are:

Central angle = 140 degrees

Diameter = 52 inches

The length of the arc is then calculated s:

$L = \frac{\theta}{360} * \pi d$

Substitute known values in the equation

$L = \frac{140}{360} * 3.142 * 52$

Evaluate the products

$L = \frac{22873.76}{360}$

Evaluate the quotient

$L = 63.54$

Hence, the arc length cleared is 63.54 inches

How to determine the area of the land cleared

The area is calculated s:

$A = \frac{\theta}{360} * \pi (d/2)^2$

Substitute known values in the equation

$A = \frac{140}{360} * 3.142 * (52/2)^2$

Evaluate the products

$A = \frac{297358.88}{360}$

Evaluate the quotient

$A = 826.00$

Hence, the area of the land cleared is 826.00 square inches

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