SOLUTION: HEMISPHERE ON HEMISPHERE.THE LARGE ONE HAS DIAMETER 22CM SMALLER 12CM WHAT IS THE TOTAL SURFACE AREA. THANK YOU

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: HEMISPHERE ON HEMISPHERE.THE LARGE ONE HAS DIAMETER 22CM SMALLER 12CM WHAT IS THE TOTAL SURFACE AREA. THANK YOU       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1011361: HEMISPHERE ON HEMISPHERE.THE LARGE ONE HAS DIAMETER 22CM SMALLER 12CM WHAT IS THE TOTAL SURFACE AREA.
THANK YOU

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

You must know that the surface area of a sphere is 4pi%2Ar%5E2.
A hemisphere is half of a sphere, this must mean that the curved surface area of a hemisphere is the surface area of a sphere divide by 2.
That is 4pi%2Ar%5E2%2F2 which gives the following expression:
Curved_+Surface_+Area+=2pi%2Ar%5E2

Total Surface Area of Hemisphere includes the circular base below the curve and its area is r%5E2%2Api+, so
Total+_Surface+_Area+_of_+Hemisphere+=2pi%2Ar%5E2%2Br%5E2%2Api+
if the large has diameter 22cm, then its radius is 11cm, and
Total+_Surface+_Area+_of_+larger_Hemisphere+=2pi%2A%2811cm%29%5E2%2B%2811cm%29%5E2%2Api+
Total+_Surface+_Area+_of_+larger_Hemisphere+=2pi%2A121cm%5E2%2B121cm%5E2%2Api+
Total+_Surface+_Area+_of_larger_+Hemisphere+=pi%2A242cm%5E2%2B121cm%5E2%2Api+
Total+_Surface+_Area+_of_larger_+Hemisphere+=363cm%5E2%2Api+
if their bases touching each other, then the area of the bases of smaller hemisphere will be already included in the area of the bases of greater hemisphere; so for smaller hemisphere we will need only curved surface area
and if the smaller has diameter 12cm, then its radius is 6cm, and
Curved_+Surface_+Area_of_smaller_+Hemisphere++=2pi%2A%286cm%29%5E2+
Curved_+Surface_+Area_of_smaller_+Hemisphere++=2pi%2A36cm%5E2+
Curved_+Surface_+Area_of_smaller_+Hemisphere++=72cm%5E2%2Api+
and, total surface area of both hemispheres will be: