Which figure has the largest surface area: a cube of edge 2, a sphere with a radius of 2, or a cylinder with a radius of 2 and height of 2?

To determine which figure has the largest surface area, we can calculate the surface area for each shape.

For the cube with an edge length of 2, the surface area can be calculated using the formula ( SA = 6a^2 ), where ( a ) is the length of an edge. Here, ( a = 2 ):

[

SA_{\text{cube}} = 6 \times (2)^2 = 6 \times 4 = 24

]

For the sphere with a radius of 2, the surface area is given by the formula ( SA = 4\pi r^2 ). With ( r = 2 ):

[

SA_{\text{sphere}} = 4\pi \times (2)^2 = 4\pi \times 4 = 16\pi \approx 50.27

]

For the cylinder with a radius of 2 and height of 2, the surface area includes the areas of the two circular bases and the side. The formula for the surface area of a cylinder is ( SA = 2\pi r(h + r) ). Substituting ( r = 2 ) and ( h =