Calculate Circle Area: Converting 7cm Diameter Using π

Q: Why can't I just use the diameter in the area formula?

The area formula $ A = \pi r^2 $ specifically requires the radius, not the diameter. The radius is the distance from center to edge, while diameter goes all the way across the circle.

Q: How do I remember that radius = diameter ÷ 2?

Think of it this way: the diameter cuts the circle in half, and each half is the radius. So radius is literally half the diameter!

Q: Should I calculate the decimal value of π or leave it as π?

For most geometry problems, leave π as π in your final answer unless specifically asked to use a decimal approximation. This keeps your answer exact!

Circle Area with Diameter-to-Radius Conversion

Given that the diameter of the circle is 7 cm

What is the area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the circle

00:03 The diameter of the circle equals twice the radius

00:07 Let's isolate radius R, this is radius R

00:13 Let's use the formula for calculating circle area

00:18 Let's substitute the radius value and solve for the area

00:33 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given that the diameter of the circle is 7 cm

What is the area?

Step-by-step solution

First we need the formula for the area of a circle:

$\pi r^2$

In the question, we are given the diameter of the circle, but we still need the radius.

It is known that the radius is actually half of the diameter, therefore:

$r=7:2=3.5$

We substitute the value into the formula.

$\pi3.5^2=12.25\pi$

Final Answer

$12.25\pi$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area of circle equals $\pi r^2$ using radius
Conversion: Radius equals diameter divided by 2, so r = 7÷2 = 3.5
Check: Verify $\pi(3.5)^2 = 12.25\pi$ matches given options ✓

Common Mistakes

Avoid these frequent errors

Using diameter directly in area formula
Don't substitute diameter (7) directly into $\pi r^2$ = $49\pi$ ! The formula requires radius, not diameter. Always divide diameter by 2 first: r = 7÷2 = 3.5, then calculate $\pi(3.5)^2 = 12.25\pi$ .

Practice Quiz

Test your knowledge with interactive questions

The center of the circle in the diagram is O.

What is the area of the circle?

FAQ

Everything you need to know about this question

Why can't I just use the diameter in the area formula?

The area formula $A = \pi r^2$ specifically requires the radius, not the diameter. The radius is the distance from center to edge, while diameter goes all the way across the circle.

How do I remember that radius = diameter ÷ 2?

Think of it this way: the diameter cuts the circle in half, and each half is the radius. So radius is literally half the diameter!

What if I get a decimal for the radius like 3.5?

Decimal radii are completely normal! Just square the decimal carefully: $3.5^2 = 3.5 \times 3.5 = 12.25$ . Keep the answer exact with $\pi$ .

Should I calculate the decimal value of π or leave it as π?

For most geometry problems, leave π as π in your final answer unless specifically asked to use a decimal approximation. This keeps your answer exact!

How can I check if my circle area answer is reasonable?

Compare your radius to the area value (without π). For radius 3.5, area coefficient should be $3.5^2 = 12.25$ , which makes sense as a reasonable size.

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