Answer:
The shaded are is [tex]113\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The shaded area is equal to the area of the semicircle minus the area of the circle inside the semicircle
step 1
Find the area of semicircle
The area of semicircle is equal to
[tex]A=\frac{1}{2}\pi r^{2}[/tex]
where
[tex]r=24/2=12\ mm[/tex] ----> the radius is half the diameter
substitute
[tex]A=\frac{1}{2}\pi(12)^{2}=72\pi\ mm^{2}[/tex]
step 2
Find the area of the circle inside the semicircle
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
where
[tex]r=12/2=6\ mm[/tex] ---> the radius of circle inside is half the radius of semicircle
substitute
[tex]A=\pi(6)^{2}=36\pi\ mm^{2}[/tex]
step 3
Find the shaded area
[tex]72\pi\ mm^{2}-36\pi\ mm^{2}=36\pi\ mm^{2}[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]36(3.14)=113.04\ mm^{2}[/tex]
3 significant figures is
[tex]113\ mm^{2}[/tex]
Answer:
113mm^2
Step-by-step explanation:
π×6²=113.097336
π×12²=452.389342
452.389342÷2=226.194671
226.194671-133.097336=113.097335
rounded to 3 s.f 113mm^2
