Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

What's the diameter of a circle with area 225π units2?

A)

15 units

B)

225 units

C)

30 units

D)

112.5 units


Sagot :

Answer:

A

Step-by-step explanation:

Please see the attached picture for the full solution.

View image Leora03

Answer:

The diameter of circle is 30 unit.

The correct answer is obtion (c) 30 unit.

Step-by-step explanation:

Given :

  • Area of circle = 225π

[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]

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.