question_answer

Refer to Design B

(iv) The difference of areas of golden and silver parts is

A) \[18\pi \,m{{m}^{2}}\]

B) \[44\pi \,m{{m}^{2}}\]

C) \[51\pi \,m{{m}^{2}}\]

D) \[64\pi \,m{{m}^{2}}\]

Correct Answer: C

Solution :

Directions (iii-iv) We have, circumference of silver part = 44 mm \[\therefore \,\,\,2\pi r=44\] \[\Rightarrow \,\,\,\,r=\frac{44}{2\times \frac{22}{7}}=7\,\,mm\] \[\therefore \,\,\,\,R=r+3=7+3=10\,\,mm\] Difference of areas \[=\pi {{R}^{2}}-\pi {{r}^{2}}\] \[=\pi \left( {{R}^{2}}-{{r}^{2}} \right)\] \[=\left( {{10}^{2}}-{{7}^{2}} \right)\pi \] \[=51\pi \,m{{m}^{2}}\]