You have combined different polygons to create a polyhedron to approximate a sphere. The sum of all the faces of the polyhedron

Question

3 years ago

14

is about 78.5 square meters. Estimate the radius of the sphere.

1 answer:

aalyn [17] · Answer 1 · 2023-02-05T21:17:23+03:00

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.

<h3>What is the surface area of sphere?</h3>

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

<h3>Radius of the sphere</h3>

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

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