A cube with a volume of 64 cubic inches is inscribed within a sphere

Question

A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2
B. 2π√3
C. 4π√2
D. 4π√3
E. 8π√2

Shruti0805 · Accepted Answer

In case of a cube inscribed within a sphere, the cube's diagonal (largest distance between any 2 points on the cube) and the sphere's diameter (largest distance between any 2 points on the sphere) should be equal.
We also know that the diagonal for a cube =  \sqrt{3}*Side

As the volume of the cube = 64 cu. inches, its sides should be 4 inches each.
Thus diagonal =  4\sqrt{3}  = Diameter of the sphere.
Thus radius =  2\sqrt{3} 
=> Circumference of the sphere =  2π*2\sqrt{3}  =  4π√3

Should be Option D.

JeffTargetTestPrep · Answer

Since the cube is inscribed in the sphere, we know that the diagonal of the cube is equal to the diameter of the sphere.
 
Since the volume of the cube is 64 and volume = side^3, the side is 4. Since the diagonal of a cube is side√3, the diagonal of the cube is 4√3.
 
Since the sphere’s diameter = 4√3, its radius is 2√3, and thus its circumference = 2πr = 2π(2√3) = 4π√3.
 
Answer: D

Abhishek009 · Answer

Certainly so, here is how the figure will look - main-qimg-4fa003c3a8c93fdbba78e63d8f8c4622.png Answer must be (D)

ThisIsWater · Answer

Hi  Bunuel ,

Sphere is 3-D object, so will there be circumference for this object or is the question asking about the projection of the sphere?

Fdambro294 · Answer

Picturing a Symmetric Cube Inscribed inside a Sphere, you can visualize that the Diameter of the Sphere that passes through the Center from Opposite Ends of the Sphere = Main Diagonal through the Center of the 3-D Cube

Volume of Cube = (s)^3 = 64

s = 4 = Edge of Cube

Main Diagonal of Cube =   ^2 + (4)^2 = (Main Diagonal)^2

d = sqrt(16 * 2 + 16)

d = 4 * sqrt(3)

d = Main Diagonal of Cube = Diameter of Sphere = 4 * sqrt(3)

the Circumference of a Sphere is given by: (pi) * (Diameter)

Circumference of Sphere = 4 * (pi) * sqrt(3)

-D-

achieveurarchive · Answer

A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

Let the side of cube = a
Volume of the cube =  a^3 =64----> a =4

Longest side of a cube = Diameter of the sphere=  \sqrt{3}*a =  \sqrt{3}*4

Circumference of the sphere = 2πr= 2π*  \sqrt{3}*2 = 4π√3

A. 2π√2
B. 2π√3
C. 4π√2
 D. 4π√3 
E. 8π√2

bumpbot · Answer

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A cube with a volume of 64 cubic inches is inscribed within a sphere

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A cube with a volume of 64 cubic inches is inscribed within a sphere

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