Radius and Diameter

Help Questions

GED Math › Radius and Diameter

Questions 1 - 10

1

What is the radius with a diameter of $\frac{\sqrt3}{2}$ ?

$\frac{\sqrt3}{4}$

$\frac{\sqrt3}{6}$

$\sqrt3$

$\sqrt6$

$\frac{\sqrt6}{4}$

Explanation

The radius is half the diameter.

Multiply the diameter by one-half.

$\frac{\sqrt3}{2} \cdot \frac{1}{2} = \frac{\sqrt3}{4}$

The answer is: $\frac{\sqrt3}{4}$

2

If a circle has an area of , what is its radius?

Explanation

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: $A=\pi \cdot r^2$ , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

$64.8= \pi \cdot r^2$

$\frac{64.8}{\pi}= r^2$

Remember that you need to take the square root in order to solve for r.

Therefore, the radius is

3

What is the radius, in inches, of a circle with a diameter of 12 inches?

Explanation

The radius is half of the diameter:

From here we plug in our diameter measure of 12 and solve for the radius:

$\frac{12}{2}=r$

4

What is the radius of a circle if it has an area of ?

Explanation

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: $A=\pi \cdot r^2$ , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

$17.3= \pi \cdot r^2$

$\frac{17.3}{\pi}= r^2$

Remember that you need to take the square root in order to solve for r.

Therefore, the radius is

5

Determine the diameter if the radius is $\frac{2}{3}x-4$ .

$\frac{4}{3}x-8$

$\frac{1}{3}x-8$

$\frac{1}{3}x-2$

$\frac{4}{3}x-2$

$\textup{The answer is not given.}$

Explanation

The diameter is double the radius.

$2(\frac{2}{3}x-4) = \frac{4}{3}x-8$

The answer is: $\frac{4}{3}x-8$

6

Find the diameter if the radius is $\sqrt5$ .

$2\sqrt5$

$\sqrt{10}$

$5\sqrt2$

Explanation

The diameter is double the radius.

Multiply the radical by two.

$d=2r = 2\cdot \sqrt5$

Do not multiply the coefficient into the radical.

The answer is: $2\sqrt5$

7

Determine the radius of the circle with a diameter of .

$3x+\frac{3}{2}$

Explanation

The radius is half the diameter. Multiply the given diameter by half.

$\frac{1}{2}(6x+3) = 3x+\frac{3}{2}$

The answer is: $3x+\frac{3}{2}$

8

Find the radius of a circle with an area of .

Explanation

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: $A=\pi \cdot r^2$ , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

$76.9= \pi \cdot r^2$

$\frac{76.9}{\pi}= r^2$

Remember that you need to take the square root in order to solve for r.

Therefore, the radius is

9

Find the radius of a circle with an area of $8\pi$ .

$2\sqrt2$

$\sqrt2$

$4\sqrt2$

$8\sqrt2$

Explanation

Write the formula for the area of a circle.

$A = \pi r^2$

Substitute the area.

$8\pi = \pi r^2$

Divide by pi on both sides.

$\frac{8\pi }{\pi}=\frac{ \pi r^2}{\pi}$

Square root both sides.

$\sqrt{r^2 }= \sqrt{8}$

$r= \sqrt8 = 2\sqrt2$

The answer is: $2\sqrt2$

10

What is the diameter of a circle with radius of 10 inches?

Explanation

The diameter is twice the radius:

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