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What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.

To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
Question 1 options:
The formula for the surface area of a sphere is 4 x pi x radius^2
The formula for the volume of a sphere is 4/3 x pi x radius^3.

Respuesta :

LammettHash
The volume will be larger than the surface area for any [tex]r[/tex] satisfying the inequality

[tex]\dfrac43\pi r^3>4\pi r^2[/tex]

Since [tex]r>0[/tex] must be true, we can divide through by [tex]4\pi r^2[/tex] to get

[tex]\dfrac13r>1\implies r>3[/tex]

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