Question

What is the height of the cone below? - 3 - 9 - 27 - 75

Answer 1

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

Answer 2

Answer:

The correct option is C) 27

Step-by-step explanation:

Consider the provided figure.  

Volume of a cone is: $V=\frac{1}{3}\pi r^2h$

The area of base of the cone is = area of circle = $\pi r^2$

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

Therefore, $45=\frac{1}{3}\pi r^2h$

and $5=\pi r^2$

Substitute the value of $\pi r^2=5$ in  $45=\frac{1}{3}\pi r^2h$

$45=\frac{1}{3}\times 5\times h$

$45\times \frac{3}{5}=h$

$h=27$

Hence, the height of the cone is 27 in.

Therefore, the correct option is C) 27