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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 :)

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 pri class=

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TaeKwonDoIsDead

Answer:

[tex]4\sqrt{\pi}[/tex]

Step-by-step explanation:

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

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

[tex]\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}[/tex]

bobiscool3698

Answer:

your answer would be 4\sqrt{\pi}

Step-by-step explanation:

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