b Equate the formula for the volume of the box with 13 and solve for the side.
C
c The side of the box and the sphere's diameter are the same length. If we label the pinata's radius r, what must the length of the box be?
A
aDimensions: (4* 4* 4) feet
Volume: 64 feet^3
B
b Radius less than 1.176 feet
C
c r=sqrt(V)/2
Practice makes perfect
a In order for the sphere to fit inside of the box, the box sides must all have a length that is at least the diameter of the sphere which is twice the radius. In other words 4 feet.
Since the box has three equal dimensions, this box is in fact a cube. Therefore, by cubing its side, we can determine its volume.
V=4^3=64 feet^3
b As we talked about in Part A, we calculate the volume of a cube with the following formula.
V=s^3
By setting V equal to 13, we can determine the length of the box side by taking the cube root of both sides.
The length of the box is 2.35 feet. This means the diameter of the pinata has to be less than 2.35 feet. This is the same thing as a radius that is less than 2.352≈ 1.176 inches.
c As we already explained, the side of the box and the sphere's diameter is the same length. If we label the maximum radius of the pinata r, the sphere's diameter and box side must both be 2r.
Therefore, if we substitute 2r in the formula for the volume of a box, we can then proceed to solve for the radius of the sphere.
