Radius

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Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

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.

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

To the nearest tenth, give the diameter of a circle with area 100 square inches.

$11.3 \textrm{ in}$

$22.6 \textrm{ in}$

$20.0 \textrm{ in}$

$5.7 \textrm{ in}$

$31.4 \textrm{ in}$

Explanation

The relationship between the radius and the area of a circle can be given as

$A = \pi r^{2}$ .

We can substitute and solve for :

$100= \pi r^{2}$

$r^{2} = \frac{100}{\pi}$

$r=\sqrt{ \frac{100}{\pi}} \approx 5.64$

Double this to get the diameter: $d \approx 5.64 \cdot2 =11.28$ , which we round to 11.3.

To the nearest tenth, give the area of a circle with diameter 17 inches.

$227.0 \textrm{ in}^{2}$

$907.9\textrm{ in}^{2}$

$289.0 \textrm{ in}^{2}$

$454.0\textrm{ in}^{2}$

$578.0\textrm{ in}^{2}$

Explanation

The radius of a circle with diameter 17 inches is half that, or 8.5 inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 8.5^{2} \approx 227.0$

To the nearest tenth, give the area of a circle with diameter $7 \frac{1}{2}$ inches.

$44.2 \textrm{ in}^{2}$

$88.4 \textrm{ in}^{2}$

$22.1 \textrm{ in}^{2}$

$176.7 \textrm{ in}^{2}$

$56.3 \textrm{ in}^{2}$

Explanation

The radius of a circle with diameter $7 \frac{1}{2}$ inches is half that, or $3 \frac{3}{4} = 3.75$ inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 3.75^{2} \approx 44.2 \textrm{ in}^{2}$

To the nearest tenth, give the area of a circle with diameter 17 inches.

$227.0 \textrm{ in}^{2}$

$907.9\textrm{ in}^{2}$

$289.0 \textrm{ in}^{2}$

$454.0\textrm{ in}^{2}$

$578.0\textrm{ in}^{2}$

Explanation

The radius of a circle with diameter 17 inches is half that, or 8.5 inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 8.5^{2} \approx 227.0$

To the nearest tenth, give the diameter of a circle with area 100 square inches.

$11.3 \textrm{ in}$

$22.6 \textrm{ in}$

$20.0 \textrm{ in}$

$5.7 \textrm{ in}$

$31.4 \textrm{ in}$

Explanation

The relationship between the radius and the area of a circle can be given as

$A = \pi r^{2}$ .

We can substitute and solve for :

$100= \pi r^{2}$

$r^{2} = \frac{100}{\pi}$

$r=\sqrt{ \frac{100}{\pi}} \approx 5.64$

Double this to get the diameter: $d \approx 5.64 \cdot2 =11.28$ , which we round to 11.3.

To the nearest tenth, give the area of a circle with diameter $7 \frac{1}{2}$ inches.

$44.2 \textrm{ in}^{2}$

$88.4 \textrm{ in}^{2}$

$22.1 \textrm{ in}^{2}$

$176.7 \textrm{ in}^{2}$

$56.3 \textrm{ in}^{2}$

Explanation

The radius of a circle with diameter $7 \frac{1}{2}$ inches is half that, or $3 \frac{3}{4} = 3.75$ inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 3.75^{2} \approx 44.2 \textrm{ in}^{2}$

Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

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