A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside

Question

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

Accepted Answer

Choice A is correct. The volume of a cube can be found by using the formula V = s 3 , where V is the volume and s is the edge length of the cube. Therefore, the volume of the given cube is V = 68 3 , or 314,432 cubic inches. The volume of a sphere can be found by using the formula V = 4 3 r 3 , where V is the volume and r is the radius of the sphere. Therefore, the volume of the given sphere is V = 4 3 34 3 , or approximately 164,636 cubic inches. The volume of the space in the cube not taken up by the sphere is the difference between the volume of the cube and volume of the sphere. Subtracting the approximate volume of the sphere from the volume of the cube gives 314,432 - 164,636 = 149,796 cubic inches. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question a-cube