Question

@jim_thompson5910

The first challenge to complete is the Penny Problem. The radio station is giving the winner of this challenge a prize pack that includes tickets to see his or her favorite band in concert. To start off the challenge, the radio station has placed pennies in a cylindrical glass jar. Each penny is 0.75 inches in diameter and 0.061 inches thick. If the cylindrical glass jar containing the pennies has a diameter of 6 inches and a height of 11.5 inches, how many pennies can fit inside the jar? You must show all work to receive credit.

Answer 1

Are they looking for the hypothetical answer or the realistic one ?
For the hypothetical answer we find the volume of the cylinder pi*3^2*11.5 and we divide it by the volume of a penny to find how many will fit.
But in reality there will be gaps so it'll be a little less than that.

Answer 2

What you do here is find the volume of the cylinder and divide by the volume of a penny.
To find the volume of a cylinder, you find the area of the circle then multiply by the height. In this case you have the diameter of the cylinder. You need the radius which is half of the diameter. 6/2= 3. The radius of the cylinder is 3.

Use the formula to find the area of a circle \[A=\pi r^{2}\] then multiply by the height to find the volume.

Answer 3

Wow that was so much different from what I said @Dscdago

Answer 4

im confused..

Answer 5

First find the area of the circle.

A=3.14(6)^2
A=3.14(36)
A=113.04.

This is the area of the cylinder. Now multiply it by the height, 11.5, to get the volume

Answer 6

Number of pennies = volume of cylinder / volume of penny

Answer 7

1299.96

Answer 8

Yes. Now you find the volume of the penny. Since they give the diameter, you need the radius. Diameter/2= radius.

Answer 9

Then apply the area of a circle formula. A=3.14(r)^2

Answer 10

@Dscdago the area you calculated is not correct.

Area = pi*r^2 = pi*(3)^2 = 28.27 inches^2

Answer 11

Which will give you a volume of V = 28.27 * 11.5 = 325.15 in^3

Answer 12

Right. For some reason, I thought the diameter was 12.

Answer 13

So the volume of the cylinder is 325.15.

Answer 14

Now for the volume of the penny
V= pi*(0.375)^2*0.061 = 0.027 in^3

If you divide the volume of the cylinder by the volume of the penny you'll get your answer.

Answer 15

325.15/0.027= number of pennies that can fit in the jar.

Answer 16

Round the answer to a number that makes sense. You can't have half a penny in a jar.