2-Dimensional Geometry - GED Math
Card 1 of 2760
Find the circumference of the circle with a diameter of
.
Find the circumference of the circle with a diameter of .
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Write the formula for the circumference of the circle.

Substitute the diameter.

The answer is: 
Write the formula for the circumference of the circle.
Substitute the diameter.
The answer is:
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Determine the circumference of the circle with a diameter of
.
Determine the circumference of the circle with a diameter of .
Tap to reveal answer
Write the formula for the circumference of the circle.

Substitute the diameter.

The answer is: 
Write the formula for the circumference of the circle.
Substitute the diameter.
The answer is:
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What is the diameter of a circle with a radius of 9?
What is the diameter of a circle with a radius of 9?
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The diameter of a circle is twice the radius:

Plug in the radius value:


The diameter of a circle is twice the radius:
Plug in the radius value:
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What is the radius of a circle given the diameter is 22?
What is the radius of a circle given the diameter is 22?
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The radius is half of the diameter, or 11.
The radius is half of the diameter, or 11.
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What angle is complementary to 10 degrees?
What angle is complementary to 10 degrees?
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Complementary angles must add up to ninety.
Subtract the given angle from 90 to find the other angle.

The answer is: 
Complementary angles must add up to ninety.
Subtract the given angle from 90 to find the other angle.
The answer is:
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Complementary angles add up to how many degrees?
Complementary angles add up to how many degrees?
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Two angles are complementary when they add up to
.
Two angles are complementary when they add up to .
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Give the area of the above circle.

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

The radius is half the diameter - that is,
- so, substituting,

or


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

,
the correct area.
The area of a circle, given its radius
, can be found using the formula
The radius is half the diameter - that is, - so, substituting,
or
The diameter of the given circle is 7, so set in the above formula:
,
the correct area.
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Let
.
Find the area of a circle with a diameter of 12in.
Let .
Find the area of a circle with a diameter of 12in.
Tap to reveal answer
To find the area of a circle, we will use the following formula:

where r is the radius of the circle.
Now, we know
. 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



To find the area of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know . 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
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While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?
While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?
Tap to reveal answer
While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?
To find circumference, use the following formula:

Now, we could find the radius and then plug it in, but if you are astute, you will see that the above formula is the same thing as:

Where d is the diameter.
So, we can plug in our diameter to find our answer:

So we can say our answer is 7.85 cm
While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?
To find circumference, use the following formula:
Now, we could find the radius and then plug it in, but if you are astute, you will see that the above formula is the same thing as:
Where d is the diameter.
So, we can plug in our diameter to find our answer:
So we can say our answer is 7.85 cm
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A circle is inscribed in square that has a side length of
, as shown by the figure below.

Find the area of the shaded region. Use
.
A circle is inscribed in square that has a side length of , as shown by the figure below.

Find the area of the shaded region. Use .
Tap to reveal answer

Since the circle is inscribed in the square, the diameter of the circle is the same length as the length of a square.
Start by finding the area of the square.

For the given square,

Now, because the diameter of the circle is the same as the length of a side of the square, we now also know that the radius of the circle must be
. Next recall how to find the area of a circle.

Plug in the found radius to find the area of the circle.

Now, the shaded area is the area left over when the area of the circle is subtracted from the area of the square. Thus, we can write the following equation to find the area of the shaded region.


Since the circle is inscribed in the square, the diameter of the circle is the same length as the length of a square.
Start by finding the area of the square.
For the given square,
Now, because the diameter of the circle is the same as the length of a side of the square, we now also know that the radius of the circle must be . Next recall how to find the area of a circle.
Plug in the found radius to find the area of the circle.
Now, the shaded area is the area left over when the area of the circle is subtracted from the area of the square. Thus, we can write the following equation to find the area of the shaded region.
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Give the circumference of the above circle. Assume each mark on each axis represents one unit.

Give the circumference of the above circle. Assume each mark on each axis represents one unit.
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The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by
, or
.
The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by , or
.
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What is the area of a circle with a diameter of
?
What is the area of a circle with a diameter of ?
Tap to reveal 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
, you can say that the radius is
.
Next, be very careful given that there is already a
in your radius. The formula for the area of a circle is:

For your data, this is:

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 , you can say that the radius is
.
Next, be very careful given that there is already a in your radius. The formula for the area of a circle is:
For your data, this is:
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Refer to the above diagram.
is equilateral;
. How many of the following statements must be true?
I)
bisects 
II)
bisects 
III) 

Refer to the above diagram. is equilateral;
. How many of the following statements must be true?
I) bisects
II) bisects
III)
Tap to reveal answer
Since corresponding parts of congruent triangles are congruent, it follows that
. Therefore,
, by definition, bisects
, and the first statement is true. A bisector of an angle of an equilateral triangle is also the perpendicular bisector of the opposite side, so the other two statements are immediate consequences.
Since corresponding parts of congruent triangles are congruent, it follows that . Therefore,
, by definition, bisects
, and the first statement is true. A bisector of an angle of an equilateral triangle is also the perpendicular bisector of the opposite side, so the other two statements are immediate consequences.
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Refer to the above diagram. Which of the following expressions gives the length of
?

Refer to the above diagram. Which of the following expressions gives the length of ?
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By the Pythagorean Theorem,






By the Pythagorean Theorem,
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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
.
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 .
Tap to reveal answer
The radius of the swimming pool is half the diameter, or 25 feet.
The area of the swimming pool is
times the square of the radius, or
square feet, or
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.
The radius of the swimming pool is half the diameter, or 25 feet.
The area of the swimming pool is times the square of the radius, or
square feet, or
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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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
.
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 .
Tap to reveal answer
The radius of the swimming pool is half the diameter, or 15 meters.
The area of the swimming pool is
times the square of the radius, or
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.
The radius of the swimming pool is half the diameter, or 15 meters.
The area of the swimming pool is times the square of the radius, or
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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What is the area of the circle with a radius of 25?
What is the area of the circle with a radius of 25?
Tap to reveal answer
Write the formula for the area of a circle.

Substitute the radius into the equation.

Simplify the equation.

The answer is: 
Write the formula for the area of a circle.
Substitute the radius into the equation.
Simplify the equation.
The answer is:
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Find the area of a circle with a radius of 12.
Find the area of a circle with a radius of 12.
Tap to reveal answer
Write the formula for the area of a circle.

Substitute the radius into the equation.

The answer is: 
Write the formula for the area of a circle.
Substitute the radius into the equation.
The answer is:
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What is the area of a circle with the diameter of 18?
What is the area of a circle with the diameter of 18?
Tap to reveal answer
Write the formula for the area of a circle.

The radius is half the diameter, or 9.
Substitute the value of the radius in to the formula.

The answer is: 
Write the formula for the area of a circle.
The radius is half the diameter, or 9.
Substitute the value of the radius in to the formula.
The answer is:
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Find the area of a circle with a radius of
.
Find the area of a circle with a radius of .
Tap to reveal answer
Write the formula for the area of a circle.

Substitute the radius into the equation.

Simplify this equation.

The answer is: 
Write the formula for the area of a circle.
Substitute the radius into the equation.
Simplify this equation.
The answer is:
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