2-Dimensional Geometry - GED Math

Card 0 of 2760

What is the diameter of a circle with a radius of 9?

Tap to see back →

The diameter of a circle is twice the radius:

Plug in the radius value:

What is the radius of a circle given the diameter is 22?

Tap to see back →

The radius is half of the diameter, or 11.

What angle is complementary to 10 degrees?

Tap to see back →

Complementary angles must add up to ninety.

Subtract the given angle from 90 to find the other angle.

The answer is:

Complementary angles add up to how many degrees?

Tap to see back →

Two angles are complementary when they add up to $90$^{\circ}$$ .

Give the area of the above circle.

Tap to see back →

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.

Let $\pi=3.14$ .

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

Tap to see back →

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$$

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

Tap to see back →

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 $10 \pi$ .

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

Tap to see back →

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$$=36\pi^3$$

Refer to the above diagram. $\Delta ABC$ is equilateral; $\Delta ABX \cong \Delta ACX$ . How many of the following statements must be true?

I) $\overline{AX}$ bisects $\angle BAC$

II) $\overline{AX}$ bisects $\overline{BC}$

III) $\overline{AX}$ \perp $\overline{BC}$

Tap to see back →

Since corresponding parts of congruent triangles are congruent, it follows that $\angle BAX \cong \angle CAX$ . Therefore, $\overline{AX}$ , by definition, bisects $\angle BAC$ , 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.

Refer to the above diagram. Which of the following expressions gives the length of $\overline{AC}$ ?

Tap to see back →

By the Pythagorean Theorem,

$AC = $$\sqrt{(AB)^{2}$$ + $(BC)^{2}$}$

$AC = $$\sqrt{(x+10)^{2}$$ + $x^{2}$}$

$AC = $\sqrt{ $x^{2}$$+ 2 \cdot x \cdot 10 $+10^{2}$ + $x^{2}$}$

$AC = $\sqrt{ $x^{2}$$+ 2 \cdot x \cdot 10 $+10^{2}$ + $x^{2}$}$

$AC = $\sqrt{ $x^{2}$$+20x +100+ $x^{2}$}$

$AC = $\sqrt{ $2x^{2}$$+20x +100 }$

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 $\pi$ .

Tap to see back →

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.

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 $\pi$ .

Tap to see back →

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.

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

Tap to see back →

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: $625 \pi$

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

Tap to see back →

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: $144\pi$

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

Tap to see back →

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: $81\pi$

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

Tap to see back →

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: $4\pi ^3$

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

Tap to see back →

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: $2500\pi$

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

Tap to see back →

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$$

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

Tap to see back →

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$$

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

Tap to see back →

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: $\pi$