Geometry - TACHS Math

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Question

Find the area of a circle with the following radius:

Answer

The area of a circle can be calculated using the following formula:

$A=\pi r^2$

In this formula the radius is denoted by the variable, .

Substitute in the known variables and solve for the circle's area.

$A=\pi \times 7^2$

$A=49\pi$

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Question

Which is equal to the radius of a circle with area $400 \pi$

Answer

The formula for the area of a circle, given its radius , is $A = \pi r^{2}$ . Replace with $400 \pi$ :

$\pi r^{2} = 400 \pi$

To find the radius , first, divide both sides by $\pi$ :

$\frac{\pi r^{2}}{\pi} = \frac{400 \pi}{\pi}$

$r^{2} = 400$

Now, find the square root of both sides. Since $400 = 20 \times 20$ , 20 is the square root of 400, so

.

The radius of the given circle is 20.

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Question

To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.

This is an example of which kind of sampling?

Answer

The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.

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Question

What is the area of a circle that has a diameter of ?

Answer

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi \times \text{radius}^2$

To find the length of the radius, divide the diameter by two.

$\text{radius}=\frac{12}{2}=6$

Now, plug it into the equation for the area of a circle.

$\text{Area of Circle}=\pi \times 6^2=36\pi=113.1$

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Question

A square has perimeter 24 feet. Give its area.

Answer

The perimeter of a figure is the sum of the lengths of its sides. A square comprises four sides of equal length, so, if the perimeter of the square is 24 feet, then each side has length

$24 \div 4 = 6$ feet.

The area of the square is equal to the length of a side multiplied by itself, so the area of this square is

$6\times6= 36$ square feet.

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Question

Jennifer wants to wallpaper her room which is made up for four rectangular walls each measuring at feet by feet. If each roll of wallpaper covers square feet of space, how many rolls of wallpaper will Jennifer need?

Answer

Start by finding out the total square footage of wallpaper needed.

Find the area of one wall. Recall that in order to find the area of a rectangle, you must multiply the length by the width.

$\text{Area of One Wall}=15 \times 12=180$

Since we have four identical walls,

$\text{Total Area of Walls}=4 \times 180 =720$

Now divide this by the amount of square feet covered by each roll of wallpaper to find how many rolls are needed.

$\text{Rolls of wallpaper needed}=\frac{720}{60}=12$

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Question

Find the circumference of a circle with the following radius:

Answer

In order to find the circumference of a circle we will use the following formula:

$C=2\pi r$

In this equation, the variable, , represent's the circle's radius.

Substitute in for the circle's radius.

$C=2\times\pi \times 4$

Simplify and solve.

$C=8\pi$

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Question

Find the perimeter of a square with the following side length:

Answer

Perimeters can be calculated by adding together the side lengths of a polygon. A square has four sides that are all the same length, therefore, we can write the following formula to solve for the perimeter.

We can rewrite this equation as the following:

In these equations the variable, , represents side length.

Substitute the known side length and solve.

$P=4\times5$

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Question

Calculate the volume of a sphere with the following radius:

Answer

We can calculate the the volume of a sphere using the following formula:

$V=\frac{4}{3}\pi r^3$

in this formula the variable, , represents the radius of the sphere.

Substitute in the known radius and calculate the volume.

$V=\frac{4}{3}\times \pi \times 3^3$

$V=\frac{4}{3}\times \pi \times 27$

$V=\frac{4}{3}\times 27\pi$

Simplify.

$V=\frac{4}{3}\times \frac{27\pi}{1}$

$V=\frac{108\pi}{3}$

Solve.

$V=36\pi$

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