SOLUTION: Calculate for the surface area of a frustum of a sphere if the diameter of its ends are 80 cm and 120 cm and the thickness is 30 cm.

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Question 1195855: Calculate for the surface area of a frustum of a sphere if the diameter of its ends are 80 cm and 120 cm and the thickness is 30 cm.
Answer by MathLover1(20849) About Me  (Show Source):
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study140122-frustum026245915134941061485

given:
the diameter of its ends are: 80cm and 120cm and the thickness is 30cm

A=pi(a^2+b^2+2Rh)
a is the radius of the smaller base->a=80cm%2F2=40cm
bis the radius of the larger base->b=120cm%2F2=60cm
R is the radius of the sphere
h is the difference in height of the two base->h=30cm

As we can see, we first have to determine the radius of the sphere R. We can find the radius from the given base diameters and frustum height.

R=sqrt%28b%5E2%2B%28b%5E2-a%5E2-h%5E2%29%2F%282h%29%29%5E2%29
R=sqrt%2860%5E2%2B%28%2860%5E2-40%5E2-30%5E2%29%2F%282%2A30%29%29%5E2%29%29
R=62.74


then the area is:
A=pi%2840%5E2%2B60%5E2%2B2%2A62.74%2A30%29
A=28162.49cm%5E2