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

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.