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kaylailkanic1487
22.02.2020 •
Mathematics
Cube A is inscribed in sphere B, which is inscribed in cube C. If the sides of cube A have length 4, what is the volume of cube C?
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Ответ:
The volume of cube C is
Step-by-step explanation:
step 1
Find the diameter of sphere B
we know that
When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere
Let
L ----> the length side of cube A
d ----> the diagonal of the base of cube A
D ---> the long diagonal of cube A
Find the diagonal of the base of cube A
Applying the Pythagorean Theorem
we have
substitute
Find the long diagonal of cube A
Applying the Pythagorean Theorem
substitute
step 2
we know that
If sphere B is inscribed in cube C, then the length side of cube C is equal to the diameter of sphere B
Let
c ----> the length side of cube C
we have that
The volume of cube C is equal to
substitute
Ответ: