pyramid-shaped gum with a square base, the company has decided to place their pyramid gum inside a clear glass giant sphere. Each piece of gum has a base measurement of 1 inch and a height of 0.75 inches. The glass sphere container has a diameter of 17.25 inches. How many pieces of Pharaoh Chewing Gum can fit inside the glass sphere? You must show all work to receive credit. gum: b=1 h=0.75 v=1/3(1)(0.75) v=0.75/5/3= 0.25 glass sphere d=17.25 v=4/3(3.14)(8.625^3) v=268.24 now we divide the gum from the sphere 2.686/0.25=10.74 pieces of gum would fit. what am i doing wrong?

Question

anonymous · Answer

my teacher says i should be using this but i dint get that answer when i use that formula The volume of the sphere would be V = (3.14)r^3 V = (3.14)(8.625^3) = 2686.25 in

matt101 · Answer

The equation for volume of a sphere is:

$$V={4 \over 3} \pi r^3$$
I haven't read through your answer in detail yet, but could it looks like you forgot to multiply by 4/3.

anonymous · Answer

oh okay thanks thats what i told my teacher but he was saying i needed to use a different formula...i guess ill redo it in the morning...again... thanks

matt101 · Answer

Hold on! I'm looking at it in more detail now :)

anonymous · Answer

i think i totally messed it up i have re don this so many times :P

matt101 · Answer

You're right about the volume of each piece of gum: 0.25 in^3.

The diameter of the sphere is 17.25 in so the radius is 8.625 in as you said.

Volume of the sphere from the equation above comes out to about 2688 in^3, which is what you got.

Aaaaand looks like the problem is in your last step - somehow you added a decimal in where it shouldn't be! You should have 2688 / 0.25 =  10 752 pieces of gum in total!

anonymous · Answer

did you use the equation you put up?

matt101 · Answer

Yes for volume of the sphere - but it's the same equation you used (even though you didn't write the 4/3 in your post). I just used a calculator that had the exact value of pi instead of using 3.14 so that's why my answer is a bit different.

anonymous · Answer

thanks again i had this problem up 3 times to day both time thry were up for over 2 hours....:D

matt101 · Answer

No problem! Sometimes it's good to have another set of eyes to find little things like that decimal. But your process for solving this question was exactly right!

anonymous · Answer

well thanks again and good night :)