The formula for the Volume of a cone is:
V = pir^2h/3
Where:
V is the Volume of the cone: 141.3"in"^3 for this problem.
r is the radius of the cone: what we are solving for in this problem.
h is the height of the cone: 15"in" for this problem.
Substituting and solving for r gives:
141.3"in"^3 = pi xx r^2 xx (15"in")/3
141.3"in"^3 = pi xx r^2 xx 5"in"
(141.3"in"^3)/color(red)(5"in") = (pi xx r^2 xx 5"in")/color(red)(5"in")
(141.3"in"^(color(red)(cancel(color(black)(3)))2))/color(red)(5color(black)(cancel(color(red)("in")))) = (pi xx r^2 xx color(red)(cancel(color(black)(5"in"))))/cancel(color(red)(5"in"))
(141.3"in"^2)/color(red)(5) = pir^2
28.26"in"^2 = pir^2
(28.26"in"^2)/color(red)(pi) = (pir^2)/color(red)(pi)
(28.26"in"^2)/color(red)(pi) = (color(red)(cancel(color(black)(pi)))r^2)/cancel(color(red)(pi))
(28.26"in"^2)/color(red)(pi) = r^2
We can use 3.1416 to estimate pi giving:
(28.26"in"^2)/color(red)(3.1416) = r^2
9"in"^2 = r^2 rounded to the nearest inch.
Now, take the square root of each side of the equation to find the radius of the cone while keeping the equation balanced:
sqrt(9"in"^2) = sqrt(r^2)
3"in" = r
r = 3"in"
The radius of the cone rounded to the nearest inch is 3 inches.
