A Right Rectangular Prism Is 3 In By 4.75 In By 20.5 In. What Is The Total Surface Area Of The Prism?A. 151.5 In$^2$B. 173.125 In$^2$C. 317.75 In$^2$D. 346.25 In$^2$
Understanding the Problem
A right rectangular prism is a three-dimensional shape with six rectangular faces. In this problem, we are given the dimensions of the prism as 3 inches by 4.75 inches by 20.5 inches. We need to find the total surface area of the prism.
What is Surface Area?
The surface area of a three-dimensional shape is the total area of its outer surface. For a right rectangular prism, the surface area can be calculated by finding the area of each face and adding them together.
Calculating the Surface Area of Each Face
To calculate the surface area of each face, we need to find the area of the two pairs of opposite faces.
- The area of the two faces with dimensions 3 inches by 4.75 inches is:
- 2 x (3 x 4.75) = 2 x 14.25 = 28.5 square inches
- The area of the two faces with dimensions 3 inches by 20.5 inches is:
- 2 x (3 x 20.5) = 2 x 61.5 = 123 square inches
- The area of the two faces with dimensions 4.75 inches by 20.5 inches is:
- 2 x (4.75 x 20.5) = 2 x 97.375 = 194.75 square inches
Calculating the Total Surface Area
Now that we have the area of each pair of opposite faces, we can add them together to find the total surface area of the prism.
- Total surface area = 28.5 + 123 + 194.75 = 346.25 square inches
Conclusion
The total surface area of the right rectangular prism is 346.25 square inches.
Answer
The correct answer is D. 346.25 in$^2$.
Additional Information
To calculate the surface area of a right rectangular prism, you can use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
In this problem, we can plug in the values as follows:
Surface Area = 2(3 x 4.75) + 2(3 x 20.5) + 2(4.75 x 20.5) Surface Area = 2(14.25) + 2(61.5) + 2(97.375) Surface Area = 28.5 + 123 + 194.75 Surface Area = 346.25 square inches
Q: What is the formula for calculating the total surface area of a right rectangular prism?
A: The formula for calculating the total surface area of a right rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Q: How do I apply the formula to calculate the total surface area of a right rectangular prism?
A: To apply the formula, you need to plug in the values of the length, width, and height of the prism into the formula. For example, if the dimensions of the prism are 3 inches by 4.75 inches by 20.5 inches, the formula would be:
Surface Area = 2(3 x 4.75) + 2(3 x 20.5) + 2(4.75 x 20.5) Surface Area = 2(14.25) + 2(61.5) + 2(97.375) Surface Area = 28.5 + 123 + 194.75 Surface Area = 346.25 square inches
Q: What if the dimensions of the prism are not given in inches? How do I calculate the total surface area?
A: If the dimensions of the prism are not given in inches, you can still calculate the total surface area by using the same formula. However, you need to make sure that all the dimensions are in the same unit. For example, if the dimensions are given in feet, you need to convert them to inches before plugging them into the formula.
Q: Can I use the formula to calculate the surface area of a prism with different shapes?
A: No, the formula is specifically designed for right rectangular prisms. If you have a prism with a different shape, you need to use a different formula to calculate its surface area.
Q: How do I calculate the surface area of a prism with a curved surface?
A: If the prism has a curved surface, you need to use a different formula to calculate its surface area. The formula for a prism with a curved surface is more complex and involves the use of calculus.
Q: Can I use a calculator to calculate the surface area of a prism?
A: Yes, you can use a calculator to calculate the surface area of a prism. However, you need to make sure that the calculator is set to the correct unit of measurement (e.g., square inches).
Q: What if I make a mistake in calculating the surface area of a prism? How do I correct it?
A: If you make a mistake in calculating the surface area of a prism, you can correct it by re-checking your calculations and making sure that you have used the correct formula and values. You can also use a calculator to double-check your calculations.
Q: Can I use the formula to calculate the surface area of a prism with negative dimensions?
A: No, the formula is not designed to handle negative dimensions. If you have a prism with negative dimensions, you need to use a different formula to calculate its surface area.
Q: Can I use the formula to calculate the surface area of a prism with fractional dimensions?
A: Yes, you can use the formula to calculate the surface area of a prism with fractional dimensions. However, you need to make sure that you have used the correct formula and values.
Conclusion
Calculating the total surface area of a right rectangular prism is a simple process that involves using the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively. By following the steps outlined in this article, you can easily calculate the total surface area of a right rectangular prism.