Math / Geometry

Question $\pi r^{2} \quad r=2-5$

Studdy Solution

STEP 1

1. The formula $\pi r^2$ is used to calculate the area of a circle.
2. The radius $r$ can vary between 2 and 5.
3. We need to calculate the area for the minimum and maximum values of $r$ .

STEP 2

1. Calculate the area for the minimum radius.
2. Calculate the area for the maximum radius.
3. Interpret the results.

STEP 3

First, calculate the area of the circle when the radius $r = 2$ .
$\text{Area} = \pi \times (2)^2$

STEP 4

Compute the square of 2:
$2^2 = 4$

STEP 5

Substitute back into the area formula:
$\text{Area} = \pi \times 4 = 4\pi$

STEP 6

Next, calculate the area of the circle when the radius $r = 5$ .
$\text{Area} = \pi \times (5)^2$

STEP 7

Compute the square of 5:
$5^2 = 25$

STEP 8

Substitute back into the area formula:
$\text{Area} = \pi \times 25 = 25\pi$

STEP 9

Interpret the results: The area of the circle varies from $4\pi$ to $25\pi$ as the radius changes from 2 to 5.
The area of the circle ranges from $4\pi$ to $25\pi$ square units.

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Question $\pi r^{2} \quad r=2-5$

Studdy Solution

STEP 1

1. The formula $\pi r^2$ is used to calculate the area of a circle.
2. The radius $r$ can vary between 2 and 5.
3. We need to calculate the area for the minimum and maximum values of $r$ .

STEP 2

1. Calculate the area for the minimum radius.
2. Calculate the area for the maximum radius.
3. Interpret the results.

STEP 3

First, calculate the area of the circle when the radius $r = 2$ .
$\text{Area} = \pi \times (2)^2$

STEP 4

Compute the square of 2:
$2^2 = 4$

STEP 5

Substitute back into the area formula:
$\text{Area} = \pi \times 4 = 4\pi$

STEP 6

Next, calculate the area of the circle when the radius $r = 5$ .
$\text{Area} = \pi \times (5)^2$

STEP 7

Compute the square of 5:
$5^2 = 25$

STEP 8

Substitute back into the area formula:
$\text{Area} = \pi \times 25 = 25\pi$

STEP 9

Interpret the results: The area of the circle varies from $4\pi$ to $25\pi$ as the radius changes from 2 to 5.
The area of the circle ranges from $4\pi$ to $25\pi$ square units.

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Questionπr2r=2−5\pi r^{2} \quad r=2-5πr2r=2−5

Studdy Solution

STEP 1

1. The formula πr2\pi r^2πr2 is used to calculate the area of a circle.2. The radius rrr can vary between 2 and 5.3. We need to calculate the area for the minimum and maximum values of rrr.

STEP 2

1. Calculate the area for the minimum radius.2. Calculate the area for the maximum radius.3. Interpret the results.

STEP 3

First, calculate the area of the circle when the radius r=2r = 2r=2.Area=π×(2)2 \text{Area} = \pi \times (2)^2 Area=π×(2)2

STEP 4

Compute the square of 2:22=4 2^2 = 4 22=4

STEP 5

Substitute back into the area formula:Area=π×4=4π \text{Area} = \pi \times 4 = 4\pi Area=π×4=4π

STEP 6

Next, calculate the area of the circle when the radius r=5r = 5r=5.Area=π×(5)2 \text{Area} = \pi \times (5)^2 Area=π×(5)2

STEP 7

Compute the square of 5:52=25 5^2 = 25 52=25

STEP 8

Substitute back into the area formula:Area=π×25=25π \text{Area} = \pi \times 25 = 25\pi Area=π×25=25π

STEP 9

Interpret the results: The area of the circle varies from 4π4\pi4π to 25π25\pi25π as the radius changes from 2 to 5. The area of the circle ranges from 4π4\pi4π to 25π25\pi25π square units.

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Question $\pi r^{2} \quad r=2-5$

1. The formula $\pi r^2$ is used to calculate the area of a circle.
2. The radius $r$ can vary between 2 and 5.
3. We need to calculate the area for the minimum and maximum values of $r$ .

1. Calculate the area for the minimum radius.
2. Calculate the area for the maximum radius.
3. Interpret the results.

First, calculate the area of the circle when the radius $r = 2$ .
$\text{Area} = \pi \times (2)^2$

Compute the square of 2:
$2^2 = 4$

Substitute back into the area formula:
$\text{Area} = \pi \times 4 = 4\pi$

Next, calculate the area of the circle when the radius $r = 5$ .
$\text{Area} = \pi \times (5)^2$

Compute the square of 5:
$5^2 = 25$

Substitute back into the area formula:
$\text{Area} = \pi \times 25 = 25\pi$

Interpret the results: The area of the circle varies from $4\pi$ to $25\pi$ as the radius changes from 2 to 5.
The area of the circle ranges from $4\pi$ to $25\pi$ square units.