Question

Express the centesimal measure as radian measure and sexagesimal measure
500g​

Answer 1

Given:-

Express the centesimal measure as radian measure and sexagesimal measure $\sf\ 500^{g}$.

Solution:-

$⇒\large\sf\ G \: = \: 500$

$⇒\large\sf\frac{D}{90} = \frac{G}{100} = \frac{2c}{\pi}$

$⇒\large\sf\frac{D}{90} = \frac{5 \cancel0 \cancel0}{1\cancel0 \cancel0} \: = \: \frac{2c}{\pi}$

$⇒\large\sf\ \frac{D}{90} \: = \: \frac{5}{1}$

$⇒\large\sf\ D \: = \: 5 \: \times \: 90 \: = \: 450$

$⇒ \: \: {\large{\boxed{\red{\sf{\therefore \: 500g \: = \: 450°}}}}}$

$⇒\large\sf\ \frac{5}{1} \: = \: \frac{2c}{\pi}$

$⇒\large\sf \ \: 5\pi \: = \: 2c$

$⇒\large\sf\ c \: = \: \frac{5\pi}{2}$

$⇒ \: \: {\large{\boxed{\red{\sf{\therefore \: 500g \: = \: \frac{5\pi c}{2} }}}}}$

$\small$

Hence, Proved!