Help me with this please ASAP
1 answer:
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Answer:
a) The length of its edge is 8 units.
b) The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Step-by-step explanation:
a) The volume of a cube (), measured in cubic units, is defined by the following expression:
(1)
Where is the side length of the cube, measured in units.
If we know that , then the length of its edge is:
The length of its edge is 8 units.
b) The volume of a sphere (), measured in cubic units, that fits snugly inside this cube is defined by:
(2)
If we know that , then the volume of the sphere is:
The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:
If we know that and
, then the fraction of the cube that is taken up by the sphere is:
The result in percentage form is calculated by multiplying the result above by 100.
The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
There's a lot of extra information here. All you are really concerned with is solving the polynomial for roots. You want t when h = 14. So let's do it:
Rearranging to make it simpler to put into a quadratic form:
Now, let's plug it into the quadratic equation:
and
Solving the quadratic gives us:
0.5899 and 0.8476
So, your answer is: h = 14 when t = 0.5899 or t = 0.8476
Rearranging to make it simpler to put into a quadratic form:
Now, let's plug it into the quadratic equation:
and
Solving the quadratic gives us:
0.5899 and 0.8476
So, your answer is: h = 14 when t = 0.5899 or t = 0.8476