d=2r√{38.5/22/7)solve step by step

Answer 1

We have the formula for the circumference of a circle:

C = 2πr

where C is the circumference and r is the radius. We also know that the diameter, d, is equal to 2r. Therefore, we can write:

C = πd

We can use this formula to solve for the radius, r. We have:

d = 2r√(38.5/(22/7))

Simplifying this expression inside the square root, we get:

d = 2r√(38.5*7/22)

d = 2r√13

Squaring both sides, we get:

d^2 = 4r^2*13

Dividing both sides by 4*13, we get:

d^2/(4*13) = r^2

Simplifying the left-hand side, we get:

d^2/52 = r^2

Taking the square root of both sides, we get:

r = √(d^2/52)

Substituting this expression for r into the formula for the circumference, we get:

C = πd = π(2r) = 2π√(d^2/52)

Simplifying this expression inside the square root, we get:

C = 2π√(d^2/(4*13)) = 2π(d/2√13)

C = πd√13/13

Therefore, the circumference of the circle is πd√13/13 and the radius is √(d^2/52), given that d = 2r√(38.5/(22/7)).