SOLUTION: the total surface area of a cone is 628 Cm2.If its slant height is 17 Cm. find the radius of the base of the cone

Algebra ->  Surface-area -> SOLUTION: the total surface area of a cone is 628 Cm2.If its slant height is 17 Cm. find the radius of the base of the cone      Log On


   

Question 981443: the total surface area of a cone is 628 Cm2.If its slant height is 17 Cm. find the radius of the base of the cone
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
A=total surface area=628cm^2; r=radius; s=slant height=17cm
.
A=pi%2Ar%2As%2Bpi%2Ar%5E2
628cm=3.14r%5E2%2B53.41r
0=3.14r%5E2%2B53.41r-628
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 3.14r%5E2%2B53.41r%2B-628+=+0) has the following solutons:

r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2853.41%29%5E2-4%2A3.14%2A-628=10740.3081.

Discriminant d=10740.3081 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-53.41%2B-sqrt%28+10740.3081+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%2853.41%29%2Bsqrt%28+10740.3081+%29%29%2F2%5C3.14+=+7.99768435275082
r%5B2%5D+=+%28-%2853.41%29-sqrt%28+10740.3081+%29%29%2F2%5C3.14+=+-25.0072384928782

Quadratic expression 3.14r%5E2%2B53.41r%2B-628 can be factored:
3.14r%5E2%2B53.41r%2B-628+=+3.14%28r-7.99768435275082%29%2A%28r--25.0072384928782%29
Again, the answer is: 7.99768435275082, -25.0072384928782. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3.14%2Ax%5E2%2B53.41%2Ax%2B-628+%29

.
So radius=7.998 cm