Question

Nestor cuts a cake with a 12-inch dameter One of the pleces he cuts has a central angle of 24° What is the area of the sice of cake? What fraction of the entire cake is this? Explain pleces he cuts has a central angle of 24 s

Answer 1

Answer:

7.54 sq. inches

Step-by-step explanation:

The cake with the cut portion has been shown in the figure below.

For calculating the area of cut part we first need to calculate the area of whole cake.

Diameter of the cake is given in the question as 12 inches.

So the area of the cake = $\pi \frac{Diameter^2}{4}$ = $3.14 \times \frac{12\times12}{4} = 113.04$ $inches^2$

Since when the central angle is 360°, the area is 113.04 square inches

So when the central angle is 24°, the area of the section will be

$\frac{113.04\times 24}{360} =7.54$

Thus area of the slice cut by Nestor is 7.54 sq. inches.

Fraction = $\frac{7.54}{113.04} = 0.07$