Question

Pls help me !!

a sector of a circle has a central angle measure of 90°, and an area of 7 square inches. what is the area of the entire circle?

area of the circle = __ square inches

Answer 1

The area of the circle is obtained by multiplying the given sector's area by 4 since the sector represents ⅔ of the circle's area. The full circle's area is therefore 28 square inches.

Step-by-step explanation:

To find the area of the entire circle when given the area of a sector, we must first understand the relationship between the sector and the full circle. The sector's central angle of 90° is ⅔ of 360°, which means the sector is ⅔ of the full circle's area. Given the sector's area is 7 square inches, we can set up a proportion where 7 square inches is to ⅔ as the full circle's area (A) is to 1 (the whole circle).

⅔ : 7 = 1 : A

To solve for A, we multiply both sides of the equation by 4:

A = 7 × 4

A = 28

So, the area of the circle is 28 square inches.

Answer 2

Answer: 28

Step-by-step explanation:

90° is 90/360 = 1/4 of a full 360° rotation. Meaning that if the central angle of the pizza slice is 90°, then we have four equal slices.

One slice is 7 square inches, so all four slices combine to 7*4 = 28 square inches