Question

A pyramid of constant density gm/cm^3 has a square base of side length 40cm, and a height of 10cm. What is the mass of the pyramid and center mass.

Answer 1

what is the volume of the pyramid ?
after you calculate the volume V the mass M will be :
M = V * density

Answer 2

v=(1/3)*b*h
v=(1/3)*10*40
v=400/3

Answer 3

mass=(400/3)*density and idk what the density is

Answer 4

i think they said : 1 gm/cm^3

Answer 5

there isnt a 1 written in the question

Answer 6

it just has the density symbol in front of that

Answer 7

so you can give numerical answer..
it will be dependent on the density value

Answer 8

not sure what u mean...

Answer 9

if the density is x then
M = (400x)/3

Answer 10

theres the answer....idk how they got it

Answer 11

v=(1/3)*b*h
b = 40 * 40 (base area)
h = 10

Answer 12

and as you can see the M is this V times the density symbol

Answer 13

yeah my professor made this so much more complicated...so then how do we find the center of mass?

Answer 14

so for the center of mass we need the intergal.
first you need to understand that the x and y of the center of mass is 0 (due to symmetry)

Answer 15

for the z point you need the integral

Answer 16

a=0 b=10

Answer 17

oh what i said is written there already

Answer 18

and isnt something (1/M)?

Answer 19

yes

Answer 20

oksy keep going:)

Answer 21

ok so now you need triple integral
zdxdydz

Answer 22

do you know what are the limits of integration ?

Answer 23

yes

Answer 24

good - you better write y and x limits as functions of z

Answer 25

zdxdydz not sure what or why u wrote this

Answer 26

triple integral

Answer 27

whats the formula to find the center of the mass? and why do we need a triple integral?