Question

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what is the volume of this oblique cone?
\\( 12\pi \\, \text{cm}^3 \\)
\\( 40\pi \\, \text{cm}^3 \\)
\\( 60\pi \\, \text{cm}^3 \\)
\\( 120\pi \\, \text{cm}^3 \\)
(image of an oblique cone with radius 6 cm and height 10 cm)

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone (including oblique cones) is given by \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height.

Step2: Identify the radius and height from the diagram

From the diagram, the radius \( r = 6\space\text{cm} \) and the height \( h=10\space\text{cm} \).

Step3: Substitute the values into the formula

Substitute \( r = 6 \) and \( h = 10 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi\times(6)^{2}\times10\\ &=\frac{1}{3}\pi\times36\times10\\ & = 12\times10\pi\\ &=120\pi\space\text{cm}^3 \end{align*}$$

\]

Answer:

\( 120\pi\space\text{cm}^3 \) (corresponding to the option with \( 120\pi\space\text{cm}^3 \))