What is the surface area of each segment?

Question

A solid sphere of diameter 10cm is divided into 12 equal segments (like a chocolate orange). What is the surface area of each segment?

Answer 1

If yu tri tu impli yu kut a plane thru the orange,

1 kut giv yu serkel, 2 kuts giv yu 2 half-serkels...same area as 1 serkel

But then yu hav the skin av 1 segment left...its area=(1/8) av surfus area av spheer

radius=5 cm, so 1 serkel=25*pi...bout 78.53975

area av spheer=4*pi*rad*rad...4*pi*25=100pi=314.15926535

But yu want 1/12 av spheer surfus area...26.179938779166665

Comments

Since each segment is the same size, each segment's surface consists of two semicircles and an area equal to 1/12 the surface area of the outer surface area of the sphere of radius 5cm. The surface area of a sphere is 4(pi)r^2, and the two semicircular sides of each segment (the straight edge of all the segments form the same diameter of the sphere) make a complete circle of area (pi)r^2. So the surface area of a segment is 4(pi)r^2/12 + (pi)r^2=(4/3)(pi)r^2=(100/3)(pi)=104.72 sq cm approx.

Answer 2

Given A solid sphere of diameter 10cm

Divided into 12 equal segments

Radius =5

1 segments = 5^2*pi=78.539

Full area of solid = 4pi5*5=100pi=314.159

So the area of a segments = 314.15/12 = 26.179

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Comments

Thanks for your answer, but to finish off your answer you needed to add 78.540 to 26.180=104.720 sq cm=(4/3)(pi)r^2.