Word problem- find the area of the circle

Question

The formula for the area of a circle is A=πr^2(to the second power) where r is the length of the radius. (The figure in front of the R is pie)

 

a. If the radius is given as 5x^3. (To the third power) Find a formula for the area in terms of the variable x.

 

b. Find the area of the circle if x=2.

 

 

please include your work, thanks in advance!! 

Answer 1

Anna,

 

You have everything you need to answer the question. Notice that in part (a) you are told in words that r = 5x³. If you put this in your formula for the area of a circle, then A = πr² = π (5x³)². Now you need to apply the rules for exponents. For any number a and exponents m and n

 

(a^m)ⁿ=a^m*n

 

Also, (ab)^m=a^m b^m.

 

To find the area at x=2 for part (b), replace x with the value of 2.

 

The area as a function of x is A(x) = 25πx⁶. See if you can figure out the steps between by using the rules for exponents.

 

Good luck!