Question

A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth. 5.81 inches 6.57 inches 7.89 inches 8.89 inches

Answer 1

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.

Answer 2

`\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`