ACT Math - Radius | Practice Hub

A square with a side length of 4 inches is inscribed in a circle, as shown below. What is the area of the unshaded region inside of the circle, in square inches?

Act_math_01

8π - 16

4π-4

8π-4

2π-4

8π-8

Explanation

Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2. Thus, the radius of the circle is half of the diameter, or 2√2. The area of the circle is then π(2√2)2, which equals 8π. Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.

Find the circumference of a circle with radius 6.

$12\pi$

$36\pi$

$6\pi$

$18\pi$

Explanation

To solve, simply use the formula for the circumference of a circle.

In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.

Thus,

$C=2\pi{r}=2*\pi*6=12\pi$

Find the area of a circle given a radius of 1.

$\pi$

$2\pi$

$4\pi$

$0.5\pi$

Explanation

To solve, simply use the formula for the area of a circle.

In this particular case, substitute one in for the radius in the following equation.

Thus,

$A=\pi{r^2}=\pi*1^2=\pi*1=\pi$

A circle has an area of $36\pi$ . Using this information find the circumference of the circle.

$12\pi$

$6\pi$

$324\pi$

$6\pi^2$

Explanation

To find the circumference of a circle we use the formula

$C=2\pi*r$ .

In order to solve we must use the given area to find the radius. Area of a circle has a formula of

$A=\pi*r^2$ .

So we manipulate that formula to solve for the radius.

$r=\sqrt{\frac{A}{\pi}}$ .

Then we plug in our given area.

$r=\sqrt{\frac{36\pi}{\pi}}=\sqrt{36}=6$ .

Now we plug our radius into the circumference equation to get the final answer.

$C=2\pi*6=12\pi$ .

A square with a side length of 4 inches is inscribed in a circle, as shown below. What is the area of the unshaded region inside of the circle, in square inches?

Act_math_01

8π - 16

4π-4

8π-4

2π-4

8π-8

Explanation

Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

Find the area of a circle given a radius of 1.

$\pi$

$2\pi$

$4\pi$

$0.5\pi$

Explanation

To solve, simply use the formula for the area of a circle.

In this particular case, substitute one in for the radius in the following equation.

Thus,

$A=\pi{r^2}=\pi*1^2=\pi*1=\pi$

A circle has an area of $36\pi$ . Using this information find the circumference of the circle.

$12\pi$

$6\pi$

$324\pi$

$6\pi^2$

Explanation

To find the circumference of a circle we use the formula

$C=2\pi*r$ .

In order to solve we must use the given area to find the radius. Area of a circle has a formula of

$A=\pi*r^2$ .

So we manipulate that formula to solve for the radius.

$r=\sqrt{\frac{A}{\pi}}$ .

Then we plug in our given area.

$r=\sqrt{\frac{36\pi}{\pi}}=\sqrt{36}=6$ .

Now we plug our radius into the circumference equation to get the final answer.

$C=2\pi*6=12\pi$ .

Find the circumference of a circle with radius 6.

$12\pi$

$36\pi$

$6\pi$

$18\pi$

Explanation

To solve, simply use the formula for the circumference of a circle.

In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.

Thus,

$C=2\pi{r}=2*\pi*6=12\pi$

Radius

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