What is the area of a circle with a radius of 8 cm?

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How to Calculate Circumference, Diameter, Area, and Radius

The circle calculator finds the area, radius, diameter and circumference of a circle labeled as a, r, d and c respectively.

For those having difficulty using formulas manually to find the area, circumference, radius and diameter of a circle, this circle calculator is just for you. The equations will be given below so you can see how the calculator obtains the values, but all you have to do is input the basic information.  The calculator does the rest.

Finding the Circumference:

The circumference is similar to the perimeter in that it is the total length needed to draw the circle.

We note the circumference as c.

c = 2πr

or

c = πd

This depends on whether or not you know the radius (r) or the diameter (d)

Let’s calculate one manually, for example.

If r = 6 cm, the the circumference is c = 2π(6) = 12π cm, if writing in terms of π. If you prefer a numerical value, the answer rounded to the nearest tenth is 37.7 cm.

Suppose you only know the diameter? If the diameter is 8 cm, then the circumference is c = π(8) = 8π or 25.1 cm, rounded to the nearest tenth.

A great thing about the formulas is that you can manipulate it to solve for an unknown if you know one of the other quantities. For example, if we know the circumference, but don’t know the radius, you can solve c = 2πr for r and get \(r = \frac{c}{2\pi}\).  Similiarly, if you want the diameter from the circumference, simply take c =πd and solve for d to get d = \(\frac{c}{\pi}\).

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Finding the Area:

Let a = area of the circle

a = πr²

If you know the diameter and not the radius, simply divide the diameter by 2 to get the radius and still use the formula above.

Again, the formula can be used to solve for the radius, if you know the area. Simply divide a by π to get r² and take the square root of
the result.

If you wish to know the diameter from the area, follow the procedure above but double the result you get for r. This is because the diameter is twice the length of the radius.

Try an example manually to get the area.

Suppose r = 5 inches

a = πr²

a = π(25) = 25π

If rounding to the nearest tenth the area is 78.5 square inches.

If you know the diameter, simply divide by 2 to get the radius and use the same formula as above.

Of course, you don’t have to go through all the manual calculations to use this calculator. Simply input the information you know and the rest will be computed for you nearly instantly.

Free

15 Questions 45 Marks 15 Mins

Given:

Radius of circle = 8 cm

An area of a circle = An area of a triangle

The base of a triangle = 8 cm 

Formula used:

If the diameter of a circle is r, then the area of a circle = π × r2 

If in a triangle, the base is b and altitude is h, then an area of triangle = (1/2) × b × h

Calculation:

An area of a circle = An area of a triangle

⇒ π × r2 = (1/2) × b × h

⇒ π × 82 = (1/2) × 8 × h

⇒ h = (π × 64 × 2)/8

⇒ h = 128 π/8

⇒ h = 16π cm

∴ The length of the corresponding altitude of the triangle is 16π​​ cm.

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Are you interested in calculating the area and circumference of a circle and the formula behind it? This is the perfect tool.

Circles are present in many places. Coins, pizzas, and vinyl disks are examples of circular objects, and the area is an essential aspect of them.

Read on if you're interested in:

• How to find the area and circumference of a circle.
• How the circumference and area of a circle relate to each other.
• How to find the area of a quarter circle.

💡 Did you know
The diameter and, therefore, the area of a pizza are critical in determining the optimum pizza size for your budget and taste. In fact, we have a pizza cost comparison calculator for your delight.

These are the formulas to calculate the circumference and area of a circle:

c = 2πr
A = πr² = πd²/4

, where:

• c stands for circumference;
• r for radius; and
• d for the diameter of the circle.

π is a constant approximately equal to 3.14159265359 and, among other things, represents the circumference-to-diameter ratio of any circle.

Suppose you want to know how to find the circumference and area of a circle with an 8 cm radius. In that case, these would be the steps to follow:

1. Use the formulas to calculate the circumference and area: c = 2πr and A = πr².
2. The circumference should equal c = 2π × 8 cm = 50.265 cm.
3. The area should equal A = π × (8 cm)² = 201.06 cm².
4. To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm².

They relate to each other by the following formula: c = 2√(πA). The equation says circumference is proportional to the square root of the area, so the bigger the circle size, the greater the circumference.

63.617 in². To find the area of any circle, given its diameter:

1. Multiply π (pi) by the diameter square: π × (9 in)² = 254.47 in².
2. Divide that result by four:
   254.47 in²/4 = 63.617 in².
3. Now you know what the area of a 9-inch circle is ✔️

To get the area of a quarter-circle:

1. Take the formula of the area of an ordinary circle: A = πr².
2. Divide that formula by four.
3. After following these steps, we can note that the area of a quarter circle is A = πr²/4.

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