Question

The figure is made up of $2$ big identical quarter circles of radius $8$ cm and a small quarter circle. Find the perimeter of the figure

• A. $33$ cm
• B. $33\pi$ cm
• C. $35$ cm
• D. $\frac{35}{2}\pi$ cm

Answer 1

The correct option is D $\frac{35}{2}\pi$ cm

As it is clearly visible from the figure

The radius of Small quarter circle=Radius of big quarter-circle $-3$

$=8-3=5cm$

Perimeter of big quarter of circle$=\frac{\pi .r}{2}$

$=\frac{3.14\times 8}{2}=12.56cm$

Perimeter of small quarter of circle

$=\frac{\pi .r}{2}=\frac{3.14\times 5}{2}=7.85cm$

Total perimeter of figure $=2$(perimeter of both quarter of circle)+perimeter of $1$ quarter of circle $+3.\left(2\right)+2.\left(8\right)$

$=2\left(12.56\right)+7.85+6+16=25.12+29.85=54.97cm=\frac{35\pi }{2}cm$