math destroyer test #13 question #3

[KristenD77]

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A cube with a volume 64in^(3) is inscribed inside a sphere. What is the surface area of the sphere?

The answer is 48pi because the radius is 2 square root of 3 BUT I don't understand where this square root of 3 came from!? I thought I would just have 2 as the radius. Please help. Math will be the death of me =*(

 

[jz123]

A cube with a volume 64in^(3) is inscribed inside a sphere. What is the surface area of the sphere?

The answer is 48pi because the radius is 2 square root of 3 BUT I don't understand where this square root of 3 came from!? I thought I would just have 2 as the radius. Please help. Math will be the death of me =*(

2 is not the radius of the sphere. 2 sq root of 3 is.
The cube is inscribed inside the sphere, so the radius of the sphere is equal to a diagonal of the cube (find the longest diagonal).

take a look at this picture

url

 

[shaedb]

Hopefully the picture I attached doesn't confuse you. Basically we're looking for the DIAMETER of the sphere by finding the distance from one corner of the cube to the other opposite corner... the only skill necessary for this problem is the pythagorean theorem as well as V(sphere)=4(pi)r^2

 

[KristenD77]

Hopefully the picture I attached doesn't confuse you. Basically we're looking for the DIAMETER of the sphere by finding the distance from one corner of the cube to the other opposite corner... the only skill necessary for this problem is the pythagorean theorem as well as V(sphere)=4(pi)r^2

got it thanks!