Solve each problem. Circumference of a CircleThe circumference of...

Question

Solve each problem. Circumference of a CircleThe circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.

Accepted Answer

Using variation techniques to solve the following problem. When the width of a curve is six ft, its parameter is 18.85 ft. Calculate the perimeter of a similar curve with the width of nine ft. We have four possible answers. A is equal to 28.275 ft. B is equal to 27.2 85 ft. C is 9.425 ft and D is 4. ft. Now to sol this, let's first assume that perimeter is directly proportional to our width. We can make the relationship help equals K multiplied by W or L. It's our perimeter. W is our width. Now K is a constant of proportionality which we will apply to every new width. So to solve this problem, we will solve for K, you know, our length is 18.85 ft when our width is equals to six ft. So we can write in this equation 18.85 ft equals K multiplied by six ft, dividing both sides by six ft, gives us K equals 18.85 ft divided by six ft. We can now apply this constant to our new width. We have our new per uh perimeter is equals to 18.85 ft divided by six ft four R K multiplied by our new width nine ft. We can then simplify by multiplying all of our numbers together. When we do that, we get a parameter of 28.275 ft. This corresponds to answer a OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each problem. Circumference of a CircleThe circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.

Key Concepts

Direct Variation

Circumference of a Circle

Proportional Relationships

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