What is the surface area of a right rectanglar prism where each edge length measures 15.10 cm
To find the surface area of a right rectangular prism, we need to find the areas of all six faces and sum them up.
The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the lengths of the sides of the rectangular prism.
Given that each edge length measures 15.10 cm, we can substitute this value into the formula:
Surface Area = 2(15.10)(15.10) + 2(15.10)(15.10) + 2(15.10)(15.10)
Simplifying this equation, we obtain:
Surface Area = 2(228.01) + 2(228.01) + 2(228.01)
Surface Area = 912.04 + 912.04 + 912.04
Surface Area = 2736.12 cm^2
Therefore, the surface area of a right rectangular prism with each edge length measuring 15.10 cm is 2736.12 cm^2.
To find the surface area of a right rectangular prism, follow these steps:
Step 1: Identify the different faces of the prism. In a right rectangular prism, you have six faces: the top and bottom, front and back, and left and right sides.
Step 2: Determine the dimensions of each face. In this case, since each edge length measures 15.10 cm, the length, width, and height of the prism are all 15.10 cm.
Step 3: Calculate the surface area of each face. Since all faces are rectangles, the surface area of a rectangle is given by the formula: Area = length × width.
Step 4: Add up the surface area of all six faces to find the total surface area.
Let's calculate:
Area of the top and bottom:
Since the length and width of the top and bottom faces are both 15.10 cm, the area of each face is:
Area = 15.10 cm × 15.10 cm = 228.01 cm²
Area of the front and back:
Since the length of the front and back faces is 15.10 cm and the width is the height of the prism (also 15.10 cm), the area of each face is:
Area = 15.10 cm × 15.10 cm = 228.01 cm²
Area of the left and right sides:
Since the length of the left and right side faces is the height of the prism (15.10 cm) and the width is the width of the prism (15.10 cm), the area of each face is:
Area = 15.10 cm × 15.10 cm = 228.01 cm²
Step 5: Add up the areas of all six faces:
Total Surface Area = 2 × (area of the top and bottom) + 2 × (area of the front and back) + 2 × (area of the left and right sides)
Total Surface Area = 2 × 228.01 cm² + 2 × 228.01 cm² + 2 × 228.01 cm²
Total Surface Area = 456.02 cm² + 456.02 cm² + 456.02 cm²
Total Surface Area = 1368.06 cm²
Therefore, the surface area of the right rectangular prism with each edge length measuring 15.10 cm is 1368.06 cm².