Question

An arc is intercepted by a central angle of 3π2 radians on a circle with a radius of 18 centimeters.

What is the exact length of the arc?

Enter your answer, in terms of π , in the box.

Answer 1

we know that

length of circumference=2*pi*r
for r=18 cm
length of circumference=2*pi*18--------> 36pi cm

if 2pi radians (full circle)------------------> has a length of 36pi cm
(3/2)pi radians---------------------------> X
X=(3/2)pi*36pi/2pi----------> x=27pi cm

the answer is
27pi cm