The arc of a sector is 352m and \$\theta = 320^0\$. Find the radius?

Arc length of a sector.

l = \$\frac{\theta}{360^\circ} \times 2 \times \pi r\$

Substitute \$22/7\$ for \$pi\$, \$320^\circ\$ for \$\theta\$ and 352 for l.

352 = \$\frac{320°}{360°} \times 2 \times \frac{22}{7} \times r\$

Cancel out common factor.

\$352 = \frac{\cancel{320°} ^{8}}{\cancel{360°} ^{9}} \times 2 \times \frac{22}{7} \times r \$

Cancel out common factor.

\$\cancel{352} ^{32} = \frac{8}{9} \times 2 \times \frac{\cancel {22} ^{2}}{7} \times r \$

Cancel out common factor.

\$\cancel{32}^4 = \frac{\cancel{8}^1}{9} \times 2 \times \frac{2}{7} \times r \$

Cancel out common factor.

\$\cancel{4}^2 = \frac{1}{9} \times \cancel{2}^1 \times \frac{2}{7} \times r \$

Cancel out common factor.

\$\cancel{2}^1 = \frac{1}{9} \times 1 \times \frac{\cancel{2^1}}{7} \times r \$

Multiply.

\$1 = \frac{1}{63} \times r \$

Solve for r.

\$ r = 63 \$

Answer

The radius is \$63 m\$.