Question

without calculating, which of the solids has the greater volume? select the correct response
2
the cylinder. the rounded interior of the cylinder allows whatever is placed inside to lay smoothly against the interior walls which allows more to fit inside the cylinder than could fit inside the cube
the cube. the cylinder could fit inside the cube and there is still room in the corners of the cube that are not in the cylinder
neither. they both have the same volume because they have the same width and height

Explanation:

The volume of a cube is calculated as \(V = s^3\) (where \(s\) is the side - length). For a cylinder, \(V=\pi r^2h\). The diameter of the cylinder is \(d = 8\) in, so the radius \(r=\frac{d}{2}=4\) in. The side - length of the cube \(s = 8\) in and the height of the cylinder \(h = 8\) in. If we consider the base areas: the base area of the cube \(A_{cube}=s^2=8\times8 = 64\) square inches, and the base area of the cylinder \(A_{cylinder}=\pi r^2=\pi\times4^2=16\pi\approx16\times3.14 = 50.24\) square inches. Since the height of both solids is the same (\(h = 8\) in), and the base area of the cube is larger than the base area of the cylinder (\(64>50.24\)), and \(V = A\times h\) (where \(A\) is the base area and \(h\) is the height for both prism - like solids: cube is a rectangular prism and cylinder is a circular prism). Also, if we imagine fitting the cylinder inside the cube, there is extra space in the corners of the cube that the cylinder does not occupy.

Answer:

The cube. The cylinder could fit inside the cube and there is still room in the corners of the cube that are not in the cylinder.