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Antoine has a solid, spherical ball of clay with a radius of 5 cm. If he shapes it into a solid, cone–shaped figure with a radius of 2 cm, what will the height of the cone be?

User AdamV
by
6.7k points

2 Answers

3 votes

Answer:125

Explanation:

User Dan Ionescu
by
6.6k points
4 votes

Answer:

Explanation:

We'll call height h.

The equations of a cone and sphere are:

Cones: 1/3 * base area * h

Spheres: 4/3 π * r³

The base area of a cone would be the area of a circle equation:

π * r² = π * 2² = 4π.

Because you're converting from sphere to cone, you would set their equations equal to each other.

1/3 * 4π * h = 4/3 π * 5³

Next, isolate h.

h = (4/3 π * 5³)/(1/3 * 4π)

h = 125

Hope this helps!

User Vetrivel PS
by
6.6k points
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