Question

The volume of a sphere is 904.32 mm^3. What is the approximate volume of a cone that has the same height and circular base with the same diameter? Use 3.14 for pi and round to the nearest hundredth.

Answer 1

Answer:

$V_c=452.16\ mm^3$

Step-by-step explanation:

Given that,

The volume of a sphere is 904.32 mm³.

The volume of a cone that has the same height and circular base with the same diameter is:

$V_c=\dfrac{1}{3}\pi r^2 \times 2r=\dfrac{2}{3}\pi r^3$

The volume of a sphere with the same radius is:

$V_s=\dfrac{4}{3}\pi r^3=2\times \dfrac{2}{3}\pi r^3$

So, the volume of sphere is :

$V_c=\dfrac{V_s}{2}\\\\V_c=\dfrac{904.32 }{2}\\\\V_c=452.16\ mm^3$

So, the volume of the cone is $452.16\ mm^3$.