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

A circle has a circumference of 31.41.

What is its radius?

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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