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You have combined different polygons to create a polyhedron to approximate a sphere. The sum of all the faces of the polyhedron is about 78.5 square meters. Estimate the radius of the sphere.

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Since the polyhedron is about 78.5 m², the radius of the sphere is 2.5 m

Since the sum of the faces of the polyhefron equals the surface area of the sphere, we find its surface area.

What is the surface area of sphere?

The surface area of sphere is given by A = 4πr² where r = radius of sphere

Radius of the sphere

Making r subject of the formula, we have

r = √(A/4π)

Given that he sum of all the faces of the polyhedron is about 78.5 square meters, this is equal to the surface area of the sphere.

So, A = 78.5 m²

Substituting this into the equation for r, we have

r = √(A/4π)

r = √(78.5 m²/4π)

r = √(19.625 m²/π)

= √(6.246 m²)

= 2.499 m

≅ 2.5 m

So, the radius of the sphere is 2.5 m

Learn more about radius of sphere here:

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