How to find the length of the diameter - High School Math
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If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?
If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?
Set the area of the circle equal to four times the circumference πr_2 = 4(2_πr).
Cross out both π symbols and one r on each side leaves you with r = 4(2) so r = 8 and therefore d = 16.
Set the area of the circle equal to four times the circumference πr_2 = 4(2_πr).
Cross out both π symbols and one r on each side leaves you with r = 4(2) so r = 8 and therefore d = 16.
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Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?
Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?
For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.
The equation for the area of a circle is A = πr2.
For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.
The equation for the area of a circle is A = πr2.
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The perimeter of a circle is 36 π. What is the diameter of the circle?
The perimeter of a circle is 36 π. What is the diameter of the circle?
The perimeter of a circle = 2 πr = πd
Therefore d = 36
The perimeter of a circle = 2 πr = πd
Therefore d = 36
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If the area of the circle touching the square in the picture above is 
, what is the closest value to the area of the square?
If the area of the circle touching the square in the picture above is
Obtain the radius of the circle from the area.
Split the square up into 4 triangles by connecting opposite corners. These triangles will have a right angle at the center of the square, formed by two radii of the circle, and two 45-degree angles at the square's corners. Because you have a 45-45-90 triangle, you can calculate the sides of the triangles to be 
, 
, and 
. The radii of the circle (from the center to the corners of the square) will be 9. The hypotenuse (side of the square) must be 
.
The area of the square is then 
.
Obtain the radius of the circle from the area.
Split the square up into 4 triangles by connecting opposite corners. These triangles will have a right angle at the center of the square, formed by two radii of the circle, and two 45-degree angles at the square's corners. Because you have a 45-45-90 triangle, you can calculate the sides of the triangles to be
The area of the square is then
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What is the diameter of a circle with a circumference of 
?
What is the diameter of a circle with a circumference of
To find the diameter we must understand the diameter in terms of circumference. The equation for the circumference of a circle is 
, where 
is the circumference and 
is the diameter. The circumference is equal to the diameter multiplied by 
.
We can rearrange 
to solve for 
.
All we have to do is plug in the circumference and divide by 
, and it will yield the diameter.
The 
s cancel and the diameter is 
.
To find the diameter we must understand the diameter in terms of circumference. The equation for the circumference of a circle is
We can rearrange
All we have to do is plug in the circumference and divide by
The
Compare your answer with the correct one above