Respuesta :
[tex]\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.4\\
V=35
\end{cases}\implies 35=\cfrac{\pi (2.4)^2 h}{3}\implies 105=5.76\pi h
\\\\\\
\cfrac{105}{5.76\pi }=h\implies 5.805467091295 \approx h\implies 5.81 \approx h[/tex]
Let's look at the formula used to find the volume of a cone.
πr²(h/3)=V
Let's fill in what we know. The volume is 35 and the radius is 2.4. Also, we're using 3.14 for pi. Let's fill this in.
2.4²(3.14)(h/3)=35
Let's find 2.4 squared.
5.76(3.14)(h/3)=35
18.0864(h/3)=35
Let's divide both sides by 18.0864.
H/3=1.93708353
Let's multiply both sides 3.
H=5.81125058
H≈5.81
So, the height is 5.81 inches.
πr²(h/3)=V
Let's fill in what we know. The volume is 35 and the radius is 2.4. Also, we're using 3.14 for pi. Let's fill this in.
2.4²(3.14)(h/3)=35
Let's find 2.4 squared.
5.76(3.14)(h/3)=35
18.0864(h/3)=35
Let's divide both sides by 18.0864.
H/3=1.93708353
Let's multiply both sides 3.
H=5.81125058
H≈5.81
So, the height is 5.81 inches.