Respuesta :

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \end{cases}\implies V=\pi r^2\cdot \cfrac{h}{3}~~ \begin{cases} \pi r^2=&area~of\\ &circular\\ &base\\ \cline{1-2} \stackrel{B}{\pi r^2}=&5\\ V=&45 \end{cases} \\\\\\ 45=5\cdot \cfrac{h}{3}\implies 135=5h\implies \cfrac{135}{5}=h\implies 27=h[/tex]

Answer:

The correct option is C) 27

Step-by-step explanation:

Consider the provided figure.  

Volume of a cone is: [tex]V=\frac{1}{3}\pi r^2h[/tex]

The area of base of the cone is = area of circle = [tex]\pi r^2[/tex]

Volume of the cone is 45 in³ and the area of base is given as 5 in²

Therefore, [tex]45=\frac{1}{3}\pi r^2h[/tex]

and [tex]5=\pi r^2[/tex]

Substitute the value of [tex]\pi r^2=5[/tex] in  [tex]45=\frac{1}{3}\pi r^2h[/tex]

[tex]45=\frac{1}{3}\times 5\times h[/tex]

[tex]45\times \frac{3}{5}=h[/tex]

[tex]h=27[/tex]

Hence, the height of the cone is 27 in.

Therefore, the correct option is C) 27

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