SOLUTION: a solid is made up of a hemisphere of radius x cm, and a cone of height x^2cm of the same radius as the hemisphere, what is the of the composite solid ?

Algebra ->  Equations -> SOLUTION: a solid is made up of a hemisphere of radius x cm, and a cone of height x^2cm of the same radius as the hemisphere, what is the of the composite solid ?      Log On


   

Question 965889: a solid is made up of
a hemisphere of radius x cm, and a
cone of height x^2cm of the same
radius as the hemisphere, what is
the of the composite solid ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Since you do not specify what you are trying to find,
we will use surface area as an example:
r=xcm; h=x^2cm
Lateral area of cone=%28pi%29%29r%28sqrt%28r%5E2%2Bh%5E2%29%29
LA=%28pi%29%28x%29sqrt%28%28x%5E2%29%2B%28x%5E2%29%5E2%29
LA=%28pi%29%28x%29sqrt%28x%5E2%2Bx%5E4%29
LA=%28pi%29%28x%29sqrt%28%28x%5E2%29%28x%5E2%2B1%29%29
LA=%28pi%29%28x%5E3%29sqrt%28X%5E2%2B1%29
.
Surface area of hemisphere=2%28pi%29r%5E2
r=xcm
SA=2%28pi%29x%5E2
.
Total surface area of composite:
Area=%28pi%29%28x%5E3%29sqrt%28X%5E2%2B1%29%2B2%28pi%29x%5E2=%28pi%29x%5E2%28%28%28x%29sqrt%28x%5E2%2B1%29%29%2B2%29