what is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18cm? A. 5832cm^3 B. 2916cm^3 C. 1944cm^3 D. 972cm^3 HEL PLEASE ASAP

Option choice C: 1944 cm^3

Step-by-step explanation:

First calculate the volume of the square, because the pyramid has to have a smaller volume then the square.  

squares volume> pyramids volume

Volume of the cube = 16^3 = 4096 cm^3

Anwser choice A is greater then the volume of the cube (5832 cm^3>4096 cm^3) and so we know it is not anwser choice A.

Next we are going to calculate the volume of a square pyramid with height=18, and side=18

Volume = 1/3 a^2h

a (base edge)= 18

a (height)= 18

V= (1/3)x(18^2)x(18)

V= 1944 Feet squared

This means that the max volume of the square pyramid is 1944 feet squared!

Option choice C: 1944 cm^3

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..