Question

The height of a cone is twice the radius of its base.

What expression represents the volume of the cone, in
cubic units?
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wilm &'m a
0208
42x

Answer 1

To find the volume of a cone is.
V=pi r^2 h/3.
So if the high(h) is twice the radius(r) the expression is.
V=pi*50^2*100/3.

Answer 2

The correct answer is option a.)
`\((2)/(3) \pi x^3\)`.

The formula for the volume
`(\(V\))` of a cone is given by
`\(V = (1)/(3) \pi r^2 h\)`, where \(r\) is the radius of the base and
`\(h\)` is the height. In this case, the height
`(\(h\))` is twice the radius
`(\(x\))`, so
`\(h = 2x\)`.

Substitute
`\(h = 2x\)` into the volume formula:

`\[V = (1)/(3) \pi r^2 (2x)\]`

Simplify further:

`\[V = (2)/(3) \pi x^3\]`

Thus, the expression representing the volume of the cone is \(\frac{2}{3} \pi x^3\).

Therefore, the correct answer is:

a.
`\((2)/(3) \pi x^3\)`

This expression accurately represents the volume of the cone in cubic units.