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

Answer:

your answer would be 4\sqrt{\pi}

Step-by-step explanation:

Answer 2

Answer:

$4\sqrt{\pi}$

Step-by-step 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:

$\pi r^2 = a^2 \\\pi(4)^2=a^2\\16\pi=a^2\\\sqrt{16\pi}=a\\ a=\sqrt{16} \sqrt{\pi} \\a=4\sqrt{\pi}$