You have a rectangular prism. The center section has been removed. The base of the original prism is 6in wide and 8in long. The height of the prism is 10in. What is the total exposed surface are of the new prism?
To find the total exposed surface area of the new prism, we need to calculate the area of the five exposed faces.
The original rectangular prism had six faces: top, bottom, front, back, left, and right. Since the center section has been removed, we are left with five exposed faces.
The base of the original prism is 6 inches wide and 8 inches long. The height of the prism is 10 inches.
To calculate the total exposed surface area, we need to find the area of each of the five exposed faces and then sum them up.
1. Top and bottom faces: The area of each top and bottom face is given by the formula length x width. So each face has an area of 8 inches x 6 inches = 48 square inches. Since there are two such faces (top and bottom), the total area is 48 square inches x 2 sides = 96 square inches.
2. Front and back faces: The area of each front and back face is given by the formula length x height. So each face has an area of 8 inches x 10 inches = 80 square inches. Since there are two such faces (front and back), the total area is 80 square inches x 2 sides = 160 square inches.
3. Left face: The left face's area is given by the formula width x height. So it has an area of 6 inches x 10 inches = 60 square inches.
Now, we can sum up the areas of the five faces to find the total exposed surface area:
96 square inches (top and bottom) + 160 square inches (front and back) + 60 square inches (left) = 316 square inches.
Therefore, the total exposed surface area of the new prism is 316 square inches.
To find the total exposed surface area of the new prism, we first need to calculate the surface area of the original prism and then subtract the area of the removed center section.
Step 1: Calculate the surface area of the original prism.
The surface area of a rectangular prism can be found using the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Given:
Width (w) = 6 inches
Length (l) = 8 inches
Height (h) = 10 inches
Plugging the values into the formula:
Surface area = 2(8 * 6) + 2(8 * 10) + 2(6 * 10)
Surface area = 2(48) + 2(80) + 2(60)
Surface area = 96 + 160 + 120
Surface area = 376 square inches
Step 2: Calculate the area of the removed center section.
Since the center section is removed, its dimensions are no longer applicable. Therefore, we do not need to calculate the area of the removed section.
Step 3: Calculate the total exposed surface area of the new prism.
The total exposed surface area of the new prism is equal to the surface area of the original prism minus the area of the removed center section.
Total exposed surface area = Surface area of original prism - Area of removed center section
Total exposed surface area = 376 square inches - 0 square inches (no section is removed)
Total exposed surface area = 376 square inches
So, the total exposed surface area of the new prism is 376 square inches.