<p>I had a question from an ACT math practice test:</p>
<p>A cube with edges 4 cm long is inscribed in a sphere. What is the radius of the sphere, in centimeters?</p>
<p>What are the options?</p>
<p>the answer should be 2 root3?</p>
<p>I’m not sure about this, but would the radius be the diagonal of the cube? In that case, you would apply the Pythagorean Theorem twice. The first time would give you the diagonal of a base and thus a leg of a vertical triangle. So that would be the root of 4^2 +4^2 (root 32) or four roots of two. The second time you would have four roots two and four as the legs and the Pythagorean Theorem would give you the diagonal of the cube. So the square root of (root 32)^2 + 4^2 is the square root of 48, simplified to 4 * square root of 3. But I might be way off base on this.</p>
<p>I think you’re right except that the diagonal of the cube is the diameter so you would just divide 4 root 3 by 2 to get the radius and that gives the correct answer (2root3). Thanks.</p>
<p>Oh, you’re right. Haha, I missed that…I always make the stupidest mistakes.</p>