What Is The Diameter Of A Circle With An Area Of 225 Π 225\pi 225 Π Square Units?A) 225 Units B) 15 Units C) 112.5 Units D) 30 Units

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Introduction

In mathematics, the area of a circle is a fundamental concept that is used to calculate the size of a circle. The area of a circle is given by the formula $A = \pi r^2$, where $A$ is the area and $r$ is the radius of the circle. In this article, we will explore how to find the diameter of a circle given its area.

Understanding the Formula

The formula for the area of a circle is $A = \pi r^2$. To find the radius of the circle, we need to rearrange the formula to isolate $r$. We can do this by dividing both sides of the equation by $\pi$ and then taking the square root of both sides.

$$r = \sqrt{\frac{A}{\pi}}$$

Finding the Radius

Now that we have the formula for the radius, we can use it to find the radius of the circle with an area of $225\pi$ square units.

$$r = \sqrt{\frac{225\pi}{\pi}}$$

Simplifying the expression, we get:

$$r = \sqrt{225}$$

$$r = 15$$

Finding the Diameter

Now that we have the radius of the circle, we can find the diameter by multiplying the radius by 2.

$$d = 2r$$

$$d = 2(15)$$

$$d = 30$$

Conclusion

In this article, we have explored how to find the diameter of a circle given its area. We used the formula for the area of a circle to find the radius and then used the radius to find the diameter. We found that the diameter of the circle with an area of $225\pi$ square units is 30 units.

Answer

The correct answer is D) 30 units.

Additional Information

• The area of a circle is given by the formula $A = \pi r^2$.
• The radius of a circle can be found by rearranging the formula to isolate $r$.
• The diameter of a circle can be found by multiplying the radius by 2.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Geometry: A Comprehensive Introduction" by Dan Pedoe

Related Topics

• Circumference of a circle
• Area of a circle
• Radius of a circle
• Diameter of a circle

Frequently Asked Questions

• Q: What is the formula for the area of a circle? A: The formula for the area of a circle is $A = \pi r^2$.
• Q: How do I find the radius of a circle? A: To find the radius of a circle, you need to rearrange the formula to isolate $r$.
• Q: How do I find the diameter of a circle? A: To find the diameter of a circle, you need to multiply the radius by 2.
  Circle Diameter Q&A =====================

Introduction

In our previous article, we explored how to find the diameter of a circle given its area. In this article, we will answer some frequently asked questions about circle diameters.

Q&A

Q: What is the formula for the diameter of a circle?

A: The formula for the diameter of a circle is $d = 2r$, where $d$ is the diameter and $r$ is the radius.

Q: How do I find the radius of a circle?

A: To find the radius of a circle, you need to rearrange the formula for the area of a circle to isolate $r$. The formula for the area of a circle is $A = \pi r^2$. Rearranging this formula to isolate $r$, we get:

$$r = \sqrt{\frac{A}{\pi}}$$

Q: What is the relationship between the diameter and the radius of a circle?

A: The diameter of a circle is twice the radius. This can be expressed mathematically as:

$$d = 2r$$

Q: Can I find the diameter of a circle if I know its circumference?

A: Yes, you can find the diameter of a circle if you know its circumference. The formula for the circumference of a circle is $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius. Rearranging this formula to isolate $r$, we get:

$$r = \frac{C}{2\pi}$$

Substituting this expression for $r$ into the formula for the diameter, we get:

$$d = 2\left(\frac{C}{2\pi}\right)$$

Simplifying this expression, we get:

$$d = \frac{C}{\pi}$$

Q: Can I find the diameter of a circle if I know its area and circumference?

A: Yes, you can find the diameter of a circle if you know its area and circumference. We can use the formula for the area of a circle to find the radius, and then use the formula for the circumference to find the diameter.

First, we can use the formula for the area to find the radius:

$$r = \sqrt{\frac{A}{\pi}}$$

Next, we can use the formula for the circumference to find the diameter:

$$d = \frac{C}{\pi}$$

Substituting the expression for $r$ into the formula for the diameter, we get:

$$d = \frac{2\pi r}{\pi}$$

Simplifying this expression, we get:

$$d = 2r$$

Q: What is the diameter of a circle with a circumference of $60\pi$ units?

A: To find the diameter of a circle with a circumference of $60\pi$ units, we can use the formula for the circumference:

$$C = 2\pi r$$

Substituting $C = 60\pi$ into this formula, we get:

$$60\pi = 2\pi r$$

Dividing both sides of this equation by $2\pi$, we get:

$$r = 30$$

Now that we have the radius, we can find the diameter by multiplying the radius by 2:

$$d = 2r$$

$$d = 2(30)$$

$$d = 60$$

Conclusion

In this article, we have answered some frequently asked questions about circle diameters. We have explored the relationship between the diameter and the radius of a circle, and we have shown how to find the diameter of a circle given its area, circumference, or both.

Additional Information

• The diameter of a circle is twice the radius.
• The formula for the diameter of a circle is $d = 2r$.
• The formula for the circumference of a circle is $C = 2\pi r$.
• The formula for the area of a circle is $A = \pi r^2$.

References

• [1] "Mathematics for Dummies" by Mark Ryan
• [2] "Geometry: A Comprehensive Introduction" by Dan Pedoe

Related Topics

• Circumference of a circle
• Area of a circle
• Radius of a circle
• Diameter of a circle

Frequently Asked Questions

• Q: What is the formula for the diameter of a circle? A: The formula for the diameter of a circle is $d = 2r$.
• Q: How do I find the radius of a circle? A: To find the radius of a circle, you need to rearrange the formula for the area of a circle to isolate $r$.
• Q: What is the relationship between the diameter and the radius of a circle? A: The diameter of a circle is twice the radius.