Question

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

A)

15 units

B)

225 units

C)

30 units

D)

112.5 units

Answer 1

The diameter of circle is 30 unit.

The correct answer is obtion (c) 30 unit.

Step-by-step explanation:

Given :

• Area of circle = 225π

`\begin{gathered}\end{gathered}`

To Find :

• Radius of circle
• Diameter of circle

`\begin{gathered}\end{gathered}`

Solution :

Finding the radius of circle by substituting the values in the formula :

`\implies{\sf{Area_((Circle)) = \pi{r}^(2)}}`

`\implies{\sf{225\pi= \pi{r}^(2)}}`

`\implies{\sf{225 * (22)/(7) = (22)/(7) * {r}^(2)}}`

`\implies{\sf{225 * \cancel{(22)/(7)} = \cancel{(22)/(7)} * {r}^(2)}}`

`\implies{\sf{225={r}^(2)}}`

`\implies{\sf{{r}^(2) = 225}}`

`\implies{\sf{r= √(225)}}`

`\implies{\sf{r= √(3 * 3 * 5 * 5)}}`

`\implies{\sf{r= \sqrt{ \underline{3 * 3} * \underline{5 * 5}}}}`

`\implies{\sf{r= {3 * 5}}}`

`\implies{\sf{r=15\:unit}}`

`\star{\underline{\boxed{\sf{\red{Radius=15\:unit}}}}}`

Hence, the radius of circle is 15 unit.

`\begin{gathered}\end{gathered}`

Now, finding the diameter of circle by substituting the values in the formula :

`\implies{\sf{Diameter = 2 * Radius}}`

`\implies{\sf{Diameter = 2 * 15}}`

`\implies{\sf{Diameter= 30 \: unit}}`

`\star{\underline{\boxed{\sf{\red{Diameter=30\:unit}}}}}`

Hence, the diameter of circle is 30 unit.

`\rule{300}{1.5}`

Answer 2

A

Explanation:

Please see the attached picture for the full solution.