Question

Calculate the radius of the circle, if it has a circumference of 16\[\pi \] feet.
(a) \[\sqrt{8}\] feet
(b) 4 feet
(c) 8 feet
(d) 16 feet
(e) 32 feet

Answer 1

Hint: The circumference of a circle is the measure of boundary which is given as \[2\pi r\]. Now equate this formula to the given value of circumference and get the value of r, which is the radius in feet.

Complete step by step solution:
Circumference of the circle is the measurement of the boundary of the circle, where r is the radius of the circle.
\[\therefore \] Circumference of the circle is given as \[2\pi r\].
We have been given the circumference of the circle as 16\[\pi \] feet.
\[\therefore \]Circumference of circle = \[2\pi r\].
Now substitute the given circumference value in the above expression.
Hence we get, \[2\pi r=16\pi \].
Now let us cancel out the like terms in the above expression and get the value of r.

\[2r=16\]
\[\Rightarrow r=\dfrac{16}{2}=8\]feet.
Thus we got the radius of the circle as 8 feet.
\[\therefore \] Option (c) is the correct answer.

Note: The circumference of the circle can also be written as \[\pi d\], where d is the diameter of the circle. We know that diameter is twice the radius. Hence we can write it as, d = 2r. Since we have to find the radius, we used the other form. We can also express 16 as 2 times 8. Then, we can directly choose option (c) if we are thorough with the concept and the formula. It will not need any calculation.