QuestionA square with area 36 is inscribed in a circle. Find the circle's circumference. A. $3 \pi$ B. $(3 \sqrt{2}) \pi$ C. $6 \pi$ D. $(6 \sqrt{2}) \pi$ E. $36 \pi$

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means the diameter of the circle is equal to the diagonal of the square. . The area of the square is given as36.
3. We need to find the circumference of the circle.

STEP 2

First, we need to find the side length of the square. We can do this by taking the square root of the area of the square.
$Side\, length = \sqrt{Area\, of\, the\, square}$

STEP 3

Now, plug in the given value for the area of the square to calculate the side length.
$Side\, length = \sqrt{36}$

STEP 4

Calculate the side length of the square.
$Side\, length = \sqrt{36} =6$

STEP 5

Now that we have the side length of the square, we can find the diagonal of the square. The diagonal of a square is given by the side length multiplied by $\sqrt{2}$ .
$Diagonal = Side\, length \\times \sqrt{2}$

STEP 6

Plug in the value for the side length to calculate the diagonal.
$Diagonal =6 \\times \sqrt{2}$

STEP 7

Calculate the diagonal of the square.
$Diagonal =6 \\times \sqrt{2} =6\sqrt{2}$

STEP 8

Now that we have the diagonal of the square, which is also the diameter of the circle, we can find the circumference of the circle. The circumference of a circle is given by $\pi$ times the diameter.
$Circumference = \pi \\times Diameter$

STEP 9

Plug in the value for the diameter to calculate the circumference.
$Circumference = \pi \\times6\sqrt{2}$

STEP 10

Calculate the circumference of the circle.
$Circumference = \pi \\times6\sqrt{2} =6\sqrt{2}\pi$ The circumference of the circle is $6\sqrt{2}\pi$ .

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QuestionA square with area 36 is inscribed in a circle. Find the circle's circumference. A. $3 \pi$ B. $(3 \sqrt{2}) \pi$ C. $6 \pi$ D. $(6 \sqrt{2}) \pi$ E. $36 \pi$

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means the diameter of the circle is equal to the diagonal of the square. . The area of the square is given as36.
3. We need to find the circumference of the circle.

STEP 2

First, we need to find the side length of the square. We can do this by taking the square root of the area of the square.
$Side\, length = \sqrt{Area\, of\, the\, square}$

STEP 3

Now, plug in the given value for the area of the square to calculate the side length.
$Side\, length = \sqrt{36}$

STEP 4

Calculate the side length of the square.
$Side\, length = \sqrt{36} =6$

STEP 5

Now that we have the side length of the square, we can find the diagonal of the square. The diagonal of a square is given by the side length multiplied by $\sqrt{2}$ .
$Diagonal = Side\, length \\times \sqrt{2}$

STEP 6

Plug in the value for the side length to calculate the diagonal.
$Diagonal =6 \\times \sqrt{2}$

STEP 7

Calculate the diagonal of the square.
$Diagonal =6 \\times \sqrt{2} =6\sqrt{2}$

STEP 8

Now that we have the diagonal of the square, which is also the diameter of the circle, we can find the circumference of the circle. The circumference of a circle is given by $\pi$ times the diameter.
$Circumference = \pi \\times Diameter$

STEP 9

Plug in the value for the diameter to calculate the circumference.
$Circumference = \pi \\times6\sqrt{2}$

STEP 10

Calculate the circumference of the circle.
$Circumference = \pi \\times6\sqrt{2} =6\sqrt{2}\pi$ The circumference of the circle is $6\sqrt{2}\pi$ .

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QuestionA square with area 36 is inscribed in a circle. Find the circle's circumference. A. 3π3 \pi3π B. (32)π(3 \sqrt{2}) \pi(32​)π C. 6π6 \pi6π D. (62)π(6 \sqrt{2}) \pi(62​)π E. 36π36 \pi36π

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means the diameter of the circle is equal to the diagonal of the square. . The area of the square is given as36.3. We need to find the circumference of the circle.

STEP 2

First, we need to find the side length of the square. We can do this by taking the square root of the area of the square.Side length=Area of the squareSide\, length = \sqrt{Area\, of\, the\, square}Sidelength=Areaofthesquare​

STEP 3

Now, plug in the given value for the area of the square to calculate the side length.Side length=36Side\, length = \sqrt{36}Sidelength=36​

STEP 4

Calculate the side length of the square.Side length=36=6Side\, length = \sqrt{36} =6Sidelength=36​=6

STEP 5

Now that we have the side length of the square, we can find the diagonal of the square. The diagonal of a square is given by the side length multiplied by 2\sqrt{2}2​.Diagonal=Side lengthtimes2Diagonal = Side\, length \\times \sqrt{2}Diagonal=Sidelengthtimes2​

STEP 6

Plug in the value for the side length to calculate the diagonal.Diagonal=6times2Diagonal =6 \\times \sqrt{2}Diagonal=6times2​

STEP 7

Calculate the diagonal of the square.Diagonal=6times2=62Diagonal =6 \\times \sqrt{2} =6\sqrt{2}Diagonal=6times2​=62​

STEP 8

Now that we have the diagonal of the square, which is also the diameter of the circle, we can find the circumference of the circle. The circumference of a circle is given by π\piπ times the diameter.Circumference=πtimesDiameterCircumference = \pi \\times DiameterCircumference=πtimesDiameter

STEP 9

Plug in the value for the diameter to calculate the circumference.Circumference=πtimes62Circumference = \pi \\times6\sqrt{2}Circumference=πtimes62​

STEP 10

Calculate the circumference of the circle.Circumference=πtimes62=62πCircumference = \pi \\times6\sqrt{2} =6\sqrt{2}\piCircumference=πtimes62​=62​πThe circumference of the circle is 62π6\sqrt{2}\pi62​π.

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QuestionA square with area 36 is inscribed in a circle. Find the circle's circumference. A. $3 \pi$ B. $(3 \sqrt{2}) \pi$ C. $6 \pi$ D. $(6 \sqrt{2}) \pi$ E. $36 \pi$

Assumptions1. The square is inscribed in the circle, which means the diameter of the circle is equal to the diagonal of the square. . The area of the square is given as36.
3. We need to find the circumference of the circle.

First, we need to find the side length of the square. We can do this by taking the square root of the area of the square.
$Side\, length = \sqrt{Area\, of\, the\, square}$

Now, plug in the given value for the area of the square to calculate the side length.
$Side\, length = \sqrt{36}$

Calculate the side length of the square.
$Side\, length = \sqrt{36} =6$

Now that we have the side length of the square, we can find the diagonal of the square. The diagonal of a square is given by the side length multiplied by $\sqrt{2}$ .
$Diagonal = Side\, length \\times \sqrt{2}$

Plug in the value for the side length to calculate the diagonal.
$Diagonal =6 \\times \sqrt{2}$

Calculate the diagonal of the square.
$Diagonal =6 \\times \sqrt{2} =6\sqrt{2}$

Now that we have the diagonal of the square, which is also the diameter of the circle, we can find the circumference of the circle. The circumference of a circle is given by $\pi$ times the diameter.
$Circumference = \pi \\times Diameter$

Plug in the value for the diameter to calculate the circumference.
$Circumference = \pi \\times6\sqrt{2}$

Calculate the circumference of the circle.
$Circumference = \pi \\times6\sqrt{2} =6\sqrt{2}\pi$ The circumference of the circle is $6\sqrt{2}\pi$ .