The area of a sector of a cicle given by the formula above, where S is the angle measure in degree of the sector and r is the radius of the cicle. Which of the following gives r in terms of A and S?

Options

A. `r=(360Api)/(S)`
B. `r=(360Z)/(Spi)`
C. `r=sqrt((360Api)/(S))`
D. `r=sqrt((360A)/(Spi))`

Answer

D

Explanation

Difficult: Medium
Category: Passport to Advanced Math/ Exponents
Strategic Advice: Don't let all the variables in a question like this intimidate you. Pretend they're simple numbers and use inverse operations to solve for the desired variable.
Getting to the Answer: To solve the equation for r, start by multiplying both sides of the equation by the only number that's in the denominator on the rights-hand side (360). Then, divide by everything that r is being multiplied by `(Spi)`:
`A=(S)/(360)timespir^(2)`
`360(A)=360((S)/(360)timespir^(2))`
`360A=Spir^(2)`
`(360A)/(Spi)=(Spir^(2))/(Spi)`
`(360A)/(Spi)=r^(2)`
Don't answer too quickly! The correct answer is not B. You're asked for r(not `r^(2)`), so take the square root of both sides of the equation to find that `r=sqrt((360A)/(Spi))`, which is (D).