SOLUTION: Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1021670: Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
Lateral Area=pi%28diameter%29%28height%29=pi%282r%29%28height%29
.
Area of base=pi%28r%5E2%29
.
3000cm%5E2=pi%282r%29%2850cm%29%2Bpi%28r%5E2%29
.
3000cm%5E2=pi%28100r%2Br%5E2%29
.
954.93=100r%2Br%5E2
.
0=r%5E2%2B100r-954.93
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 1r%5E2%2B100r%2B-954.93+=+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=%28100%29%5E2-4%2A1%2A-954.93=13819.72.

Discriminant d=13819.72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-100%2B-sqrt%28+13819.72+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%28100%29%2Bsqrt%28+13819.72+%29%29%2F2%5C1+=+8.77865258748281
r%5B2%5D+=+%28-%28100%29-sqrt%28+13819.72+%29%29%2F2%5C1+=+-108.778652587483

Quadratic expression 1r%5E2%2B100r%2B-954.93 can be factored:
1r%5E2%2B100r%2B-954.93+=+1%28r-8.77865258748281%29%2A%28r--108.778652587483%29
Again, the answer is: 8.77865258748281, -108.778652587483. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B100%2Ax%2B-954.93+%29

.
ANSWER: The radius would be approximately 8.78 centimeters.
.