Which explanation can be used to derive the formula for the circumference of a circle?
find the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. use this quotient to set up an equation to showing the ratio of the circumference over the diameter equals to ππ . then rearrange the equation to solve for the circumference. substitute 2 times the radius for the diameter.
find the length of the radius and the length of the diameter. then, write a ratio comparing the length of the radius to the diameter. multiply the ratio by ππ and set it equal to the circumference.
find the length of the diameter. square this length and write a ratio for the square of the diameter to the radius. set the ratio equal to the circumference.
find the relationship between the area and the radius. then set up an equation showing the ratio of the area to the radius. substitute the area for 3 times the circumference. finally, rearrange the equation to solve for the circumference.
2. regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. the polygon area can be expressed in terms of the area of a triangle.
let s be the side length of the polygon,
r be the hypotenuse of the right triangle,
h be the height of the triangle, and
n be the number of sides of the regular polygon.
polygon area = n(12sh)n(12sh)
n=6
which statement is true?
as s increases, h approaches r so that rhrh approaches r².
as n increases, h approaches r so that rhrh approaches r².
as r increases, h approaches r so that rhrh approaches r².
as h increases, s approaches r so that rhrh approaches r².
3.what is the area of a circle whose radius is 6 ft?
6π6π ft²
9π9π ft²
36π36π ft²
72π72π ft²
4.the circumference of a circle is 7Ď€7Ď€ m.
what is the area of the circle?
3.5π3.5π m²
12.25π12.25π m²
14π14π m²
49π49π m²
Answers: 1
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Which explanation can be used to derive the formula for the circumference of a circle?
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