SOLUTION: The slant height of the cone is 25 units and its lateral surface area is 550 square units. Find the radius of the cone. (Round the answer to the nearest tenth.)

Algebra ->  Surface-area -> SOLUTION: The slant height of the cone is 25 units and its lateral surface area is 550 square units. Find the radius of the cone. (Round the answer to the nearest tenth.)       Log On


   

Question 610773: The slant height of the cone is 25 units and its lateral surface area is 550 square units. Find the radius of the cone. (Round the answer to the nearest tenth.)

Found 2 solutions by solver91311, ewatrrr:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The formula for the Lateral Surface Area of a cone given the radius of the base and the slant height is:



Substitute the values you know (since you are going to round to the nearest 10th, 3.14 for is plenty close enough]



Solve for

John

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Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 





Surface Area = Area of Base + lateral Area

 550 = pi%2Ar%5E2+%2B+pi%2Ar%2As where s is the slant height

 550/3.14 = r%5E2+%2B+25r or

 r^2 + 25r - 175.1 = 0

r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

r+=+%28-25+%2B-+sqrt%28+1325.4+%29%29%2F%282%29+

   r = 5.7 units     (tossing out negative solution for length)