Answer:
The diameter of circle is 30 unit.
The correct answer is obtion (c) 30 unit.
Step-by-step explanation:
Given :
[tex]\begin{gathered}\end{gathered}[/tex]
To Find :
- Radius of circle
- Diameter of circle
[tex]\begin{gathered}\end{gathered}[/tex]
Solution :
Finding the radius of circle by substituting the values in the formula :
[tex]\implies{\sf{Area_{(Circle)} = \pi{r}^{2}}}[/tex]
[tex]\implies{\sf{225\pi= \pi{r}^{2}}}[/tex]
[tex]\implies{\sf{225 \times \dfrac{22}{7} = \dfrac{22}{7} \times {r}^{2}}}[/tex]
[tex]\implies{\sf{225 \times \cancel{\dfrac{22}{7}} = \cancel{\dfrac{22}{7}} \times {r}^{2}}}[/tex]
[tex]\implies{\sf{225={r}^{2}}}[/tex]
[tex]\implies{\sf{{r}^{2} = 225}}[/tex]
[tex]\implies{\sf{r= \sqrt{225}}}[/tex]
[tex]\implies{\sf{r= \sqrt{3 \times 3 \times 5 \times 5}}}[/tex]
[tex]\implies{\sf{r= \sqrt{ \underline{3 \times 3} \times \underline{5 \times 5}}}}[/tex]
[tex]\implies{\sf{r= {3 \times 5}}}[/tex]
[tex]\implies{\sf{r=15\:unit}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Radius=15\:unit}}}}}[/tex]
Hence, the radius of circle is 15 unit.
[tex]\begin{gathered}\end{gathered}[/tex]
Now, finding the diameter of circle by substituting the values in the formula :
[tex]\implies{\sf{Diameter = 2 \times Radius}}[/tex]
[tex]\implies{\sf{Diameter = 2 \times 15}}[/tex]
[tex]\implies{\sf{Diameter= 30 \: unit}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Diameter=30\:unit}}}}}[/tex]
Hence, the diameter of circle is 30 unit.
[tex]\rule{300}{1.5}[/tex]
