Answer: The total surface area of the toy chest is 212.754 square feet (ft²)
Explanation:
The total surface area of the rectangular prism can be found using the formula:
SA = 2 ( lw + lh + wh ),
where: l = 8.25 ft, w = 6 ft, h = 3 ft
The width of the prism is found with the diameter of the cylinder, and the height of the prism is equal to the radius, which is half of the diameter of the cylinder.
In this case, the top of the rectangular prism is covered, so we'll just account for one of them, which would look like:
2 ( wh+ lh ) + lw
Now, the surface area of a full cylinder is:
SA = 2 * pi * radius * height
But, in this case, the cylinder is cut in half, so we just divide the total surface area by 2.
SA = pi * radius * height
pi = 3.14159
radius = 3
height = 8.25
All together, the formula for the total surface area would look like:
2 ( wh+ lh ) + lw + (pi * radius * height)
∴ if we plug in the values we get:
2 ( 8.25 * 3 + 6 * 3 ) + 8.25 * 6 + ( 3.14159 * 3 * 8.25 ) =
212.754 feet squared (ft²)