What is the area and perimeter of a semicircle with a diameter of 10 cm?

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Answer 1 · 2017-07-01T02:37:43

See below.

Okay, you will need to know these two formulas to solve:

$A = π r^{2}$ $A = pir^2$ and $C = 2 π r$ $C=2pir$ ,

where $A$ $A$ is the area of the circle, $C$ $C$ is the circumference (or perimeter), and $r$ $r$ is the radius.

Also, $d = 2 r$ $d = 2r$ , where d is diameter.

Now, plug in $10$ $10$ cm (the diameter) into this equation to find the radius of the given circle (as $d$ $d$ ).

$d = 2 r$ $d = 2r$
$(10) = 2 r$ $(10) = 2r$
$r = 5 cm$ $r= 5" cm"$

Now, you can use the radius that you found and the first two equations that I mentioned to find the area and perimeter of the circle.

$A = π r^{2}$ $A = pir^2$
$A = π {(5 cm)}^{2}$ $A=pi(5" cm")^2$

$C = 2 π r$ $C=2pir$
$C = 2 π (5 cm)$ $C=2pi(5" cm")$

Now, you can enter this into your calculator, where $π$ $pi$ is about $3.14$ $3.14$ .

After doing so, you should get the two following numbers:

$A = 78.5 {cm}^{2}$ $A=78.5" cm"^2$
$C = 30.9 cm$ $C=30.9" cm"$

These are your two answers!

I hope that helped!