Geometry - Pre-Algebra

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Question

What is the circumference of a circle with a radius equal to ?

Answer

The circumference can be solved using the following equation:

$C=2r\pi=2(7)\pi=14\pi$

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Question

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius inches; the width of the rectangle is $8 \pi$ inches. What is the length of the rectangle?

Answer

The circumference of a circle with radius inches is

$C = 2 \pi r = 2 \pi \cdot 30 = 60 \pi$ inches.

The perimeter of the rectangle is therefore $60 \pi$ inches. To find its length, substitute $W = 8\pi$ and $P = 60\pi$ into the equation and solve for :

$2 L + 2 \cdot 8 \pi = 60 \pi$

$2 L + 16 \pi = 60 \pi$

$2 L + 16 \pi - 16 \pi = 60 \pi - 16 \pi$

$2 L =44 \pi$

$2 L \div 2=44 \pi \div 2$

$L = 22\pi$ inches

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Question

What is the circumference of a circle with an area equal to $81\pi$ ?

Answer

Using the area, solve for the radius:

$A=r^2\pi$

$81\pi=r^2\pi$

Divide by $\pi$ :

Take the square root:

$\sqrt{81}=9=r$

Plug this radius into the formula for the circumference:

$C=2r\pi=2(9)\pi=18\pi$

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Question

Becky's house is surrounded by a circular lake that Becky runs around each day. If Becky wants to figure out the distance she runs around the lake, what formula should Becky use?

Answer

Becky should use the circumfrence formula to find the distance she runs of a lake.

Correct Answer: $C=2\Pi r$

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Question

What is the circumference of a circle with a radius of ?

Answer

The circumference can be solved using the following equation:

$C=2r\pi$

Where represents the radius. Therefore, when we substitute our radius in we get:

$=2(8)\pi =16\pi$

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Question

Determine the circumference of the circle if the radius is 20.

Answer

Write the formula for circumference.

$C=2\pi r$

Substitute the radius and solve.

$C=2\pi(20) = 40\pi$

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Question

Given the area of the circle is $9\pi$ , what is the circumference of the circle?

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area.

$9\pi=\pi r^2$

Write the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi (3) = 6\pi$

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Question

Find the circumference of the circle with a diameter of $2\pi$ .

Answer

Write the formula for the circumference of a circle.

$C=\pi D = 2\pi r$

Substitute the diameter.

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

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Question

Find the circumference of a circle with an area of $\pi^2$ .

Answer

Write the area formula in order to find the radius.

$A=\pi r^2$

Substitute the area.

$\pi ^2=\pi r^2$

$r^2=\pi$

$r=\sqrt{\pi}$

Write the circumference formula.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{\pi}$

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Question

Determine the circumference of the circle if the radius is $2\pi$ .

Answer

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the radius into the formula.

$C=2\pi (2\pi) = 4\pi ^2$

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Question

Find the circumference of a circle with a radius of $\sqrt2$ .

Answer

Write the formula to find the circumference of a circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{2}$

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Question

Find the circumference of a circle with an area of 5.

Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area to find the radius.

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

$5=\pi r^2$

$\frac{5}{\pi }=r^2$

$r=\sqrt{\frac{5}{\pi}}$

Write the formula to find the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{\frac{5}{\pi}}$

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Question

If $\pi = 3.14$ find the circumference of a circle with a diameter of 10 inches.

Answer

To solve, we will use the formula for circumference of a circle. The formula is

$C = 2 \pi r$

where $r = \text{ radius}$ . We know that the diameter of the circle is 10 inches. To find the radius, we simply divide by 2.

Therefore,

We know $\pi = 3.14$ , so we will substitute. We get

$C = 2 \cdot 3.14 \cdot 5 \text{ inches}$

$C = 31.4 \text{ inches}$

Therefore, the circumference of the circle is 31.4 inches.

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Question

Find the circumference of a circle with a radius of 6cm.

Answer

The formula to find the circumference of a circle is

$C = \pi d$

where d is the diameter. We know the radius is 6cm. We also know to find the diameter, we take two times the radius. Therefore, the diameter is 12cm. So, substituting into the formula, we get

$C = \pi \cdot 12$

or

$C = 12\pi$

Therefore, the circumference of the cirlce is $12\pi$ .

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Question

A circle has a radius of . What is its circumference?

Answer

The formula for the circumference of a circle is

$C=2\pi r$ .

So, we simply plug in the radius of in order to solve for the circle's circumference:

$C=2\pi (19)$

$C=38\pi$

Therefore, the circumference of ths circle is $38\pi$ .

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Question

What is the distance around a silo, if the distance from the center of the silo to the outside is ?

Answer

What is the distance around a silo, if the distance from the center of the silo to the outside is ?

Picture a silo, its base is a circle.

This problem want the circumference of that circle. It gives us the distance from the center to the outside of the circle, aka the radius.

Find circumference via the following formula:

$Circumference=2 \pi r$

$C=2*8 \pi =16\pi m$

So the distance is:

$16\pi m$

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Question

Alfredo ran laps around his track. He had just learned in math about circumference and was wondering what the circumference of his circular track was. He knows that the diameter of his track is 100 feet. What is the circumference of Alfredo's track?

Answer

The only thing that needs to be known for this question is the equation for circumference which is:

$\pi$

Therefore your answer to this problem is simply

$100\pi$

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Question

Michelle wants to put a fence up around all four sides of her rectangular garden, which measures 10 ft. long and 15 ft. wide. How long will her fence be?

Answer

Since the perimeter marks out the distance around a shape, you can imagine yourself walking around a shape to find the perimeter. For a rectangle, you would walk the same length twice (once on each side) and the same width twice (once on each side). That's why you multiply both the length and the width by 2.

To find the perimeter, use the following formula:

Step 1: insert length and width into the formula

Step 2: solve

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Question

Susy's yard is 32 yards by 17 yards. What is the total perimeter of her yard?

Answer

Recall, the perimeter of a rectangle = 2length + 2width

Using the values given to us in the problem:

$\small Perimeter = (234)+(217) = 64+34 = 98$

Thus, the perimeter is 98 yards.

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Question

Sally has a rectangular garden that is surrounded by a 6ft-wide and 8ft-long fence. However, she wants to expand her garden so that it is twice as wide and twice as long. What is the new perimeter of her garden?

Answer

We know the original garden is a 6ft by 8ft rectangle. sally wants to expand her garden so that the new rectangle is twice as long and twice as wide, so the new dimensions are 12ft by 16ft.

The perimeter of a rectangle with these dimensions is

122 +162 = 56.

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