SOLUTION: You have 100 square meters of material. Which will hold more volume, a sphere or a cube made from that much material? How much more? Thank you Nick.

Algebra ->  Volume -> SOLUTION: You have 100 square meters of material. Which will hold more volume, a sphere or a cube made from that much material? How much more? Thank you Nick.      Log On


   

Question 57459: You have 100 square meters of material. Which will hold more volume, a sphere or a cube made from that much material? How much more? Thank you Nick.
Answer by rcmcc(152) About Me  (Show Source):
You can put this solution on YOUR website!
to solve this we must make 2 simple equations,
to calculate the volume of a cube you multiply the length width and height, however because they are all the same length it is X^3
the area of a cube is lxWx6sides, so X^2*6=100sqm.
first we must calculate the length of the side (x) by dividing 100/6 and square routing by 2.
so.
x^2=100/6
x^2=16.6666
x=16.6666^(1/2)
x=4.082482904m
do not round this number as we must use its value to calculate the volume of the cube.
the volume is 4.082482904^3
the volume of the cube is 68.0413....m cubed
so the volume is 68m cubed.
you do the same process for a sphere, the area equation is 4pi r^2 and the volume is (4/3)pi r^3
we are trying to isolate r
so 100=4(3.14...)r^2
100/4=3.14...r^2
25/3.14...=r^2
7.957747155=r^2
7.957747155^(1/2)=r
r=2.820947918m.
now you can calculate the volume of the sphere,
(4/3)pi(2.820947918)^3
volume of the sphere is 94.03m cubed
so the sphere holds more volume than the square.