We need to find the height of both objects and the radius of the cylinder
For the rectangular prism, we have
2.5 = (base area)(height
2.5 = (2 *1) * height
2.5 = 2 * height divide both sides by 2
1.25 = height
The surface area = base area + side area =
(2* 1) + 2 * (1.25)( 2 + 1) = 2 + 2.5 ( 3) = 9.5 sq ft
So.....the total cost = 9.5 * 1.30 = $12.35
For the cylinder we have that
2.5 = base area * height
2.5 = 2.5 * height divide both sides by 2.5
1 = height
The radius can be found as
2.5 = pi * radius^2
2.5 = 3.14 * radius^2 divide both side by 3.14
2.5 /3.14 = radius^2 take the square root
√[2.5 / 3.14 ] = radius
The total surface area = base area + side area = 2.5 + 2 * pi * radius * height =
2.5 + 2 * 3.14 * √[2.5/3.14) * 1 =
2.5 + 2*3.14√[2.5/3.14]
So....the total cost for the cylinder =
1.30 ( 2.5 + 2* 3.14√[2.5/3.14] ) = $10.54
So....the cylinder is cheaper
