SOLUTION: Hi A solid hemisphere concave up has a radius of 11cm . Placed on top of it is another solid hemisphere concave down with radius 6cm. Find the total surface area. My answer

Question 1166787: Hi
A solid hemisphere concave up has a radius of 11cm . Placed on top of it is another solid hemisphere concave down with radius 6cm.
Find the total surface area.
My answer is 760cm^2 the textbook says 1253cm^2 who is correct.
Thanks
Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

Your book is correct.

You have the area of the concave up hemisphere +
area of concave down hemisphere +
area of the "ring" exposed on the flat part of the lower hemisphere (which is the area of a circle of radius 11cm minus the area of a circle with radius 6cm).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the book is correct.

here's why.

the surface area of a sphere is equal to 4 * pi * r^2

the surface area of a hemisphere would be half of that.

therefore, the surface area of the larger hemisphere is equal to 4 * pi * 11^2 / 2 = 760.2654222, .....

and the surface area of the smaller hemisphere is equal to 4 * pi * 6^2 / 2 = 226.1946711.

the sum of their areas is equal to 986.4600932 square centimeters.

but, that's not the total surface area that's exposed.

the base of each hemispheres is a circle whose area is equal to pi * r^2.

the area of the bases that is exposed is the area of the base of the larger hemisphere minus the area of the base of the smaller hemisphere.

that exposed area is equal to pi * 11^2 minus pi * 6^2 = 267.0353756 square centimeters.

add that to 986.4600932 to get a total exposed area of 1253.495469 square centimeters.

you can round as required.

here's my diagram of the situation as i see it.

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