Question

If the shaded cross sections of the solids have the same area, which of the following corresponds to the value of a: the side length of the base of the square prism?

answer choices: 2, 4, √2pi, 4√pi

Please help i'm having trouble with this problem. Thanks :)

Answer 1

your answer would be 4\sqrt{\pi}

Explanation:

Answer 2

`4√(\pi)`

Explanation:

• The cross section of a sphere is a circle with area
  `\pi r^2`, where radius is given as 4
• The cross section of the cube is a square with area
  `a^2`, where a is side length of square

The circle area = the square area. Thus we have:

`\pi r^2 = a^2 \\\pi(4)^2=a^2\\16\pi=a^2\\√(16\pi)=a\\ a=√(16) √(\pi) \\a=4√(\pi)`