\boxed{10\pi x^2}
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- The lateral surface area of a cone is given by:
- where $ r = 2x $ and $ l = 5x $. Substituting:
- A = \pi (2x)(5x) = 10\pi x^2
- Question: A quantum algorithm designer is modeling a 3D lattice where each node is a cube of side $ x $. A diagonal connects two opposite vertices of the cube. What is the length of this space diagonal in terms of $ x $?
- The space diagonal $ d $ of a cube with side length $ x $ is given by the 3D Pythagorean theorem:
- d = \sqrt{x^2 + x^2 + x^2} = \sqrt{3x^2} = x\sqrt{3}
