Answer:
The area of circle is 254.34 in².
Step-by-step explanation:
Given :
- [tex]\small\purple\bull[/tex] Diameter of circle = 18 in
To Find :
- [tex]\small\purple\bull[/tex] Radius of circle
- [tex]\small\purple\bull[/tex] Area of circle
Using Formulas :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
- [tex]\blue\star[/tex] R = radius
- [tex]\blue\star[/tex] D = diameter
[tex]\star{\small{\underline{\boxed{\sf{\pink{Area_{(Circle)} = \pi{r}^{2} }}}}}}[/tex]
- [tex]\blue\star[/tex] π = 3.14
- [tex]\blue\star[/tex] r = radius
Solution :
Here we have given that diameter of circle is 18 in. So, finding the radius of circle :
[tex]\implies{\sf{Radius = \dfrac{D}{2}}}[/tex]
[tex]\implies{\sf{Radius = \dfrac{18}{2}}}[/tex]
[tex]\implies{\sf{Radius = \cancel{\dfrac{18}{2}}}}[/tex]
[tex]\implies{\sf{Radius = 9 \: in}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Radius = 9 \: in}}}}}[/tex]
Hence, the radius of circle is 9 in.
[tex]\rule{200}2[/tex]
Now, we know the radius of circle is 9 in. So, finding the area of circle by substituting the values in the formula :
[tex]\implies{\sf{Area_{(Circle)} = \pi{r}^{2}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9)}^{2}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9 \times 9)}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times (81)}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314}{100} \times 81}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314 \times 81}{100}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{25434}{100}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 254.34 \: {in}^{2} }}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{Area_{(Circle)} = 254.34 \: {in}^{2}}}}}}}[/tex]
Hence, the area of circle is 254.34 in².
[tex]\rule{300}{1.5}[/tex]
