Question

The diameter of a circle is 105 cm less than the circumference. What is the diameter of circle ?.

• A. $44cm$
• B. $46cm$
• C. $48cm$
• D. $49cm$

Answer 1

The correct option is D $49cm$

Formula to calculate the circumference of circle C $=2\pi r$

$=\pi D$

D, the diameter of circle is $C-105$

$\therefore C=n(C-105)=\pi C-105\pi$

$\Rightarrow nC-C=105\pi :C(\pi -1)=105\pi$

$\Rightarrow C=\frac{105\pi }{\pi -1}$ and $C=\pi D$ then

$\Rightarrow \pi D=\frac{105\pi }{\pi -1}$

$\Rightarrow D=\frac{105}{\pi -1}=49$ (taking $\pi =\frac{22}{7}$)

Diameter $=49cm.$

Hence, the answer is $49cm.$