$\begingroup$

What is the Perimeter of shaded region in semicircle if four small semicircles have radii of 1,2,3,4 respectively?

a. 10 $\pi$ b. 20 $\pi$ c. 40 $\pi$ d. 60 $\pi$

enter image description here

$\endgroup$1

4 Answers

$\begingroup$

Add all radii and then multiply by $\pi$:

$$\pi[1+2+3+4+(1+2+3+4)]$$

$\endgroup$$\begingroup$

Since the perimeter of a half-circle is just $\pi$ times the diameter, the perimeter of the shaded region equals the perimeter of the whole big circle. The big circle has radius $10$, hence the answer is $\color{red}{20\pi}$.

$\endgroup$$\begingroup$

perimeter of circle = 2πr (or πd, where d-> diameter)

perimeter of shaded region = (sum of perimeter of all circles) / 2

how many circles are there ? 

a. circle with radius 1 (perimeter = 2πr = 2π) b. circle with radius 2 (perimeter = 2πr = 4π) c. circle with radius 3 (perimeter = 2πr = 6π) d. circle with radius 4 (perimeter = 2πr = 8π) e. circle with radius (1 + 2 + 3 + 4) (perimeter = 2πr = 20π)

perimeter of shaded region 

= (sum of perimeter of all circles) / 2 = (a + b + c + d) / 2 = (2π + 4π + 6π + 8π + 20π) / 2 = 20π
$\endgroup$$\begingroup$

It`s A because (1 + 2 + 3 + 4) = 10 hence 10pi is perimeter.

$\endgroup$1