Question

question: 2
a lemon tart has a circular top with a radius of 5 inches. gina cuts a piece from the tart in the shape of a sector formed by a central angle with measure 27°.
what is the area, in square inches, of the top of the piece that gina cut out?
a. ( a=\frac{27}{180}(25 pi) )
b. ( a=\frac{27}{360}(10 pi) )
c. ( a=\frac{27}{180}(10 pi) )
d. ( a=\frac{27}{360}(25 pi) )

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360^{\circ}}\times\pi r^{2}\), where \(\theta\) is the central angle and \(r\) is the radius of the circle.

Step2: Calculate the area of the whole circle

Given \(r = 5\) inches, the area of the whole circle \(A_{circle}=\pi r^{2}=\pi\times5^{2}=25\pi\) square inches.

Step3: Substitute the values into the sector - area formula

Here, \(\theta = 27^{\circ}\) and \(A_{circle}=25\pi\). Substituting into the formula \(A=\frac{\theta}{360^{\circ}}\times A_{circle}\), we get \(A=\frac{27}{360}(25\pi)\).

Answer:

D. \(A = \frac{27}{360}(25\pi)\)