Math

QuestionFind the area of a semicircle with a radius of 4 mm. Use the formula: Area = 12πr2\frac{1}{2} \pi r^2.

Studdy Solution

STEP 1

Assumptions1. The radius of the semicircle is4 millimeters. . We are asked to find the area of the semicircle.
3. The formula for the area of a full circle is \pi r^ where rr is the radius of the circle.
4. The area of a semicircle is half the area of a full circle.

STEP 2

First, we need to find the area of a full circle with the given radius. We can do this by plugging the given radius into the formula for the area of a full circle.
Areacircle=πr2Area_{circle} = \pi r^2

STEP 3

Now, plug in the given value for the radius to calculate the area of the full circle.
Areacircle=π(mm)2Area_{circle} = \pi (mm)^2

STEP 4

Calculate the area of the full circle.
Areacircle=π(4mm)2=16πmm2Area_{circle} = \pi (4mm)^2 =16\pi mm^2

STEP 5

Now that we have the area of the full circle, we can find the area of the semicircle by dividing the area of the full circle by2.
Areasemicircle=Areacircle/2Area_{semicircle} = Area_{circle} /2

STEP 6

Plug in the value for the area of the full circle to calculate the area of the semicircle.
Areasemicircle=16πmm2/2Area_{semicircle} =16\pi mm^2 /2

STEP 7

Calculate the area of the semicircle.
Areasemicircle=16πmm2/2=πmm2Area_{semicircle} =16\pi mm^2 /2 =\pi mm^2The area of the semicircle is πmm2\pi mm^2.

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