Area of a Circle - GED Math

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Question

The diameter of a circle is . Find the area.

Answer

The formula for the area of a circle is

$area = \Pi r^2$

with standing for radius.

In this problem, however, you are given the diameter, not the radius. You therefore need to solve for the radius first. This is simple. The diameter is twice the length of the radius, so if the diameter is , the radius is . .

Once you have the radius, you can plug it into the formula for the area of a circle, and solve.

$\Pi r^2 = \Pi (5)^2 = 25\Pi$

So, the area of the circle is $25\Pi$ .

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Question

You and your friends are ordering pizza for your Friday night Mathathon. You decide to order three pizzas, each 16" in diameter. Find the area of each pizza to the nearest tenth.

Answer

You and your friends are ordering pizza for your Friday night Mathathon. You decide to order three pizzas, each 16" in diameter. Find the area of each pizza to the nearest tenth.

First, let's convert our diameter to radius:

$r=\frac{d}{2}=\frac{16 in}{2}=8 in$

Next, use the following formula to solve for Area.

$A=\pi r^2= \pi (8in)^2=64 \pi in ^2 \approx 201.1 in^2$

So, our answer is:

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Question

A $90 ^{\circ }$ arc of a circle has length $7 \pi$ . Which expression gives its area?

Answer

A $90 ^{\circ }$ arc of the circle is one fourth of the circle, so the length of the arc is

$L = \frac{1}{4}C$ ,

where is its circumference.

Since $L = 7 \pi$ , substitute as follows:

$\frac{1}{4}C = 7 \pi$

Multiply both sides by 4:

$\frac{1}{4}C \cdot 4 = 7 \pi \cdot 4$

$C = 28 \pi$

The radius of a circle is its circumference divided by $2 \pi$ , so

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

$r= \frac{28 \pi }{2\pi} = 14$

Substitute this for in the formula

$A = \pi r^{2}$

to get

$A = \pi \cdot 14^{2} = \pi \cdot 14 \cdot 14 = 196 \pi$ ,

the correct choice.

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Question

Give the area of the above circle.

Answer

The area of a circle, given its radius , can be found using the formula

$A = \pi r^{2}$

The radius is half the diameter - that is, $r = \frac{d}{2}$ - so, substituting,

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

or

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

$A = \left ( \frac{d^{2}}{4} \right )\pi$

The diameter of the given circle is 7, so set in the above formula:

$A = \left ( \frac{7^{2}}{4} \right )\pi$

$A = \frac{49}{4} \pi$ ,

the correct area.

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Question

Let $\pi=3.14$ .

Find the area of a circle with a diameter of 12in.

Answer

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know $\pi=3.14$ . We also know the diameter is 12in. We know the diameter is two times the radius, so the radius is 6in. Now, we can substitute. We get

$A = 3.14 \cdot (6\text{in})^2$

$A = 3.14 \cdot 36\text{in}^2$

$A = 113.04\text{in}^2$

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Question

Give the circumference of the above circle. Assume each mark on each axis represents one unit.

Answer

The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by $\pi$ , or $10 \pi$ .

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Question

What is the area of a circle with a diameter of $12\pi$ ?

Answer

Be careful on several counts for this question. First, remember that you need the radius for calculating area. Therefore, since you know that the diameter is $12\pi$ , you can say that the radius is $6\pi$ .

Next, be very careful given that there is already a $\pi$ in your radius. The formula for the area of a circle is:

$A=\pi r^2$

For your data, this is:

$A=\pi (6\pi)^2=\pi * 36\pi^2=36\pi^3$

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Question

Use 3.14 for pi and round your answer to the nearest hundredth.

Find the area of a circle with a diameter of 12cm.

Answer

First we need to recall that the formula for area of a circle is

$Area=r^{2}\cdot \pi$

Where is radius and $\pi$ is 3.14

The circe we are working with has a diameter of 12. The diameter is twice the length of the radius, so to find the radius we cut it in half, and we get 6cm.

Now we can plug our radius and pi into our equation and solve for the area

$Area=(6cm)^{2}\cdot3.14$

Following order of operations, first we need to address the exponent. Any number to the second power (squared) is that number times itself one time (in this case it is 6x6)

$Area=36cm^{2}\cdot3.14$

Next we multiply

$Area=113.04cm^{2}$

Since we multiplied two terms whose units are in cm, our answer is in centimeters squared.

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Question

Find the area of a circle given that the distance from its center to its edge is 6.25 meters.

Answer

Find the area of a circle given that the distance from its center to its edge is 6.25 meters.

Area of a circle is given by:

$A=\pi r^2$

We know that our radius is 6.25 m, given that this is the distance from the center to the edge.

Plug in and solve.

$A=\pi (6.25m)^2=122.7185 m^2\approx 122.72m^2$

So our answer is

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Question

A circular swimming pool at an apartment complex has diameter 50 feet. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of ten square yards. How many square yards will the manager need to buy?

Use 3.14 for $\pi$ .

Answer

The radius of the swimming pool is half the diameter, or 25 feet.

The area of the swimming pool is $\pi$ times the square of the radius, or

$\pi \times 25 ^{2} = 3.14 \times 625 = 1,962.5$ square feet, or

$1,962.5 \div 9 \approx 218$ square yards.

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 220 square yards.

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Question

A circular swimming pool at an apartment complex has diameter 30 meters. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of ten square meters. How many square yards will the manager need to buy?

Use 3.14 for $\pi$ .

Answer

The radius of the swimming pool is half the diameter, or 15 meters.

The area of the swimming pool is $\pi$ times the square of the radius, or

$\pi \times 15 ^{2} = 3.14 \times 225 = 706.5$ square meters.

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 710 square meters.

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Question

What is the area of the circle with a radius of 25?

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (25)^2$

Simplify the equation.

$A=\pi (25)(25) = 625 \pi$

The answer is: $625 \pi$

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Question

Find the area of a circle with a radius of 12.

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (12)^2 = 144\pi$

The answer is: $144\pi$

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Question

What is the area of a circle with the diameter of 18?

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter, or 9.

Substitute the value of the radius in to the formula.

$A=\pi( 9)^2 = 81\pi$

The answer is: $81\pi$

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Question

Find the area of a circle with a radius of $2\pi$ .

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (2\pi)^2$

Simplify this equation.

$A=\pi (2\pi)(2\pi) = 4\pi ^3$

The answer is: $4\pi ^3$

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Question

Find the area of a circle with a circumference of $100 \pi$ .

Answer

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$100\pi=2\pi r$

Divide by $2\pi$ on both sides.

$\frac{100\pi}{2\pi}=\frac{2\pi r}{2\pi}$

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (50)^2 = 2500\pi$

The answer is: $2500\pi$

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Question

Find the area of a circle with a diameter of 22cm.

Answer

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the diameter of the circle is 22cm. We also know the diameter is two times the radius. Therefore, the radius is 11cm.

So, we can substitute. We get

$A = \pi \cdot (11\text{cm})^2$

$A = \pi \cdot 121\text{cm}^2$

$A = 121\pi \text{ cm}^2$

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Question

Find the area of a circle with a radius of 8in.

Answer

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the radius of the circle is 8in. So, we can substitute. We get

$A = \pi \cdot (8\text{in})^2$

$A = \pi \cdot 64\text{in}^2$

$A = 64\pi \text{ in}^2$

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Question

Determine the area of a circle in square feet with a radius of 12 inches.

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Convert the radius to feet. There are 12 inches in a foot.

This means the radius in feet is 1.

Substitute the radius in feet to obtain the area in feet squared.

$A=\pi (1\textup{ ft})^2 = \pi \textup{ ft}^2$

The answer is: $\pi$

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Question

Determine the area of a circle if the radius is .

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi(20)^2 = 400\pi$

The answer is: $400\pi$

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