Question

The height of a cone is twice the radius of its base.What expression represents the volume of the cone, incubic units?2x0 21x2O 20x347x3Mark this and retumSave and ExitNextSubmit

Answer 1

Let V1 be the volume of the large sphere:

`V_1=(4)/(3)\pi\cdot r^3_l_{}`

and let V2 be the volume of the smaller sphere:

`V_2=(4)/(3)\pi\cdot r^3_s`

since the radius of the large sphere is twice the radius of the small sphere, we have the following equation:

`r_l=2r_s`

if we do this substitution on the first equation, we get the following:

`\begin{gathered} V_1=(4)/(3)\pi(2r_s)^3=(4)/(3)\pi\cdot8r^3_s=8\cdot((4)/(3)\pi\cdot r^3_s)=8\cdot V_2 \\ \Rightarrow V_1=8\cdot V_2_{} \end{gathered}`

therefore, the volume of the larger sphere is 8 times the volume of the smaller sphere