Question

Find the area of the 1/4 circle when the radius is 8

Answer 1

64pi / 4 = 16pi, or 50.27

Explanation:

We use the area formula:

π * r^2 = Area

Substitute in 8 for r to get 64pi

Then all you have to do is divide 64pi by 4 to find a quarter of the area of the circle, which is 16pi. Or if you want rounded to nearest tenth, 50.27

Answer 2

Method 1 (using the area of a whole circle and dividing by 4)

First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:

A = π ×r²

= π ×8²

= 64π (leave the answer as an exact solution as this need to be divided by 4).

So all you need to do now is divide the answer by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.

Method 2 (using ¼ πr²)

Substitute r = 8 directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 8².

A = 50.3 cm²

As you can see it gives exactly the same answer as method 1.