Given the cone as shown below
The volume of a cone is evaluated as
[tex]\begin{gathered} \text{Volume = }\frac{1}{3}^{}\times\pi\text{ }\times r^2\times h \\ \text{where} \\ r\text{ is the radius of the circular base of the cone} \\ h\text{ is the height of the cone} \end{gathered}[/tex]
From the above figure,
radius of the circular base = YZ
height of the cone = XY
To evaluate the radius and height of the cone:
XYZ is a right-angled triangle.
Thus, using trigonometric ratios, we can evaluate XY and YZ.
height of the cone:
[tex]\begin{gathered} \sin \text{ 54 =}\frac{XY}{XZ} \\ \Rightarrow\sin \text{ 54 = }\frac{h}{15} \\ h=15\times\sin \text{ 54 = 15 }\times0.8090 \\ \Rightarrow h=12.14\text{ cm} \end{gathered}[/tex]
radius of the cone:
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