Question

The volume of a right cone is defined as V=πr2h / 3
. What is the simplified form of the expression that represents the cube of this volume, V^3
? Treat the constant π
as you would a variable in your answer.(1 point)

Answer 1

so what's the answer simplified?

Answer 2

To find the simplified form of the cube of the volume of a right cone, where the volume \( V \) is given by

\[
V = \frac{\pi r^2 h}{3},
\]

we need to calculate \( V^3 \):

\[
V^3 = \left(\frac{\pi r^2 h}{3}\right)^3.
\]

Now, applying the power of a fraction rule and the power rule, we have:

\[
V^3 = \frac{(\pi r^2 h)^3}{3^3} = \frac{(\pi^3)(r^2)^3(h)^3}{27}.
\]

Simplifying \( (r^2)^3 \) gives us:

\[
(r^2)^3 = r^{2 \cdot 3} = r^6.
\]

Thus, we can rewrite \( V^3 \):

\[
V^3 = \frac{\pi^3 r^6 h^3}{27}.
\]

So, the simplified form of the expression that represents the cube of the volume \( V^3 \) is:

\[
V^3 = \frac{\pi^3 r^6 h^3}{27}.
\]

Answer 3

The simplified form of the cube of the volume \( V^3 \) of a right cone is:

\[
V^3 = \frac{\pi^3 r^6 h^3}{27}.
\]

This is the most simplified expression, where \( \pi \), \( r \), and \( h \) are treated as variables.