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

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

volleyballlover55 · Answer

@johnweldon1993

kittiwitti1 · Answer

Okay, let's first focus on the context.$$\text{"can hold"}=Volume_{cone}=35\text{ in}^{3}$$So the volume of the cone is 35 cubic inches... now add that to the formula.$$V_{cone}=\frac{1}{3}\times base\times height$$

volleyballlover55 · Answer

whats the base and height?

kittiwitti1 · Answer

Since the base is a circle, you have to incorporate the area of a circle into this equation which is $A_{circle}=\pi r^{2}$

kittiwitti1 · Answer

The problem wants you to use 3.14 instead of $\pi$, and the radius given is $r=2.4\text{ in}$. So the area of the circle becomes $A_{circle}=3.14\times(2.4)^{2}$.

Now we need to put this back into the original formula for the cone's volume:$$V_{cone}=\frac{1}{3}\times A_{circle}\times h$$$$V_{cone}=\frac{1}{3}\times(3.14\times(2.4)^{2})\times h$$ I set height as a variable, $h$

kittiwitti1 · Answer

You have the volume of the cone as 35 cubic inches: $$35=\frac{1}{3}\times3.14(5.76)\times h$$Now all you need to do is isolate the h to find its value.

kittiwitti1 · Answer

@volleyballlover55 everything good? I hope my explanation made sense o.o

volleyballlover55 · Answer

yes it did so whats the final answer?

kittiwitti1 · Answer

Did you try and solve for $h$?

volleyballlover55 · Answer

let me try... give me a sec..

volleyballlover55 · Answer

i got 5.8!

volleyballlover55 · Answer

so its A?

kittiwitti1 · Answer

Sorry, I'm working it out

volleyballlover55 · Answer

ok..

kittiwitti1 · Answer

Yup. I got 5.8 as well.$$\text{Good job!}$$

volleyballlover55 · Answer

ok next!
A can of chicken stock measures 3.5 inches in diameter and is 5 inches tall. What is the volume of the can? Use 3.14 for pi. Round your answer to the nearest hundredth.

 38.50 cubic inches
 48.08 cubic inches
 92.46 cubic inches
 192.33 cubic inches

kittiwitti1 · Answer

Sorry, I've got to study for my final exam ; - ;

kittiwitti1 · Answer

I'll give you a hint though, since you have the formula
d = 3.5, so radius is half of that

kittiwitti1 · Answer

put the radius in the "base" section (area of circle) and then calculate the whole thing

sorry, gtg! ; - ;