Question

The volume of a sphere is 904.32 mm3. What is the approximate volume of a cone that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth.
A. 301.44 mm2A. 301.44 mm2

B. 452.16 mm2B. 452.16 mm2

C. 904.32 mm2C. 904.32 mm2

D. 1,808.64 mm2

Answer 1

The volume of the cone is 452.16 cubic mm if the cone has the same height and a circular base with the same diameter option (B) is correct.

What is a sphere?

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

$\rm V = \dfrac{4}{3} \pi r^3$

We have the volume of the sphere = 904.32 cubic mm

$\rm 904.32 = \dfrac{4}{3} \pi r^3$

After solving:

r = 5.99 ≈ 6 mm

Diameter of the sphere = height of the cone = 2(6) = 12 mm

Volume of the cone:

$\rm v=\pi r^2\dfrac{h}{3}$

$\rm v=\pi (6)^2\dfrac{12}{3}$

Take π = 3.14

After calculating:

v = 452.16 cubic mm

Thus, the volume of the cone is 452.16 cubic mm if the cone has the same height and a circular base with the same diameter option (B) is correct.

Learn more about the sphere here:

brainly.com/question/11374994

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