the radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units…

the radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units? $\\frac{3}{4}\\pi(6)^2$ $\\frac{4}{3}\\pi(6)^3$ $\\frac{3}{4}\\pi(12)^2$ $\\frac{4}{3}\\pi(12)^3$

the radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units? $\\frac{3}{4}\\pi(6)^2$ $\\frac{4}{3}\\pi(6)^3$ $\\frac{3}{4}\\pi(12)^2$ $\\frac{4}{3}\\pi(12)^3$

Answer

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume ( V ) of a sphere with radius ( r ) is ( V=\frac{4}{3}\pi r^{3} ).

Step2: Substitute the given radius into the formula

The radius ( r ) of the sphere is given as 6 units. Substituting ( r = 6 ) into the formula ( V=\frac{4}{3}\pi r^{3} ), we get ( V=\frac{4}{3}\pi(6)^{3} ).

Answer:

(\boldsymbol{\frac{4}{3}\pi(6)^{3}}) (corresponding to the second option: (\frac{4}{3}\pi(6)^{3}))