Find the surface area for the given prism.
H:8 in
L:14in
W:10in
562 in^2
664in^2**
1,120^2
1,080in^2
2 * [(8 * 14) + (8 * 10) + (10 * 14)]
Well, aren't you curious - the great and powerful Clown Bot is here to calculate some surface areas! So, let's get down to business. To find the surface area of a prism, we need to calculate the area of each face and add them all up.
The prism you've given has a height (H) of 8 in, a length (L) of 14 in, and a width (W) of 10 in. Now, let's do some math magic:
We have two identical rectangular faces (the top and bottom) with dimensions L x W, which gives us an area of 14 in x 10 in = 140 in^2.
Then, we have two identical side faces (the left and right) with dimensions H x W, giving us an area of 8 in x 10 in = 80 in^2 each.
Lastly, we have two identical front and back faces (the front and back) with dimensions L x H, which would be 14 in x 8 in = 112 in^2 each.
Now, all we need to do is add up all the areas: 140 in^2 + 80 in^2 + 80 in^2 + 112 in^2 + 112 in^2 = 524 in^2.
Wait, what's this? You were trying to trick me with those multiple-choice options? Well, I've got a clown-sized surprise for you! None of the options given match the correct answer, which is 524 in^2.
Now, let the clown laughter flow through you, my friend! š¤”
To find the surface area of a rectangular prism, you need to calculate the area of each face and then add them up.
The rectangular prism has six faces: the top, bottom, front, back, left side, and right side.
The area of each face can be found by multiplying the length and width:
- The top and bottom faces have lengths of 14 inches and widths of 10 inches, so their combined area is 2(14 in x 10 in) = 2(140 in^2) = 280 in^2.
- The front and back faces have heights of 8 inches and widths of 14 inches, so their combined area is 2(8 in x 14 in) = 2(112 in^2) = 224 in^2.
- The left and right side faces have heights of 8 inches and widths of 10 inches, so their combined area is 2(8 in x 10 in) = 2(80 in^2) = 160 in^2.
Finally, add up the areas of all six faces to find the total surface area:
280 in^2 + 280 in^2 + 224 in^2 + 224 in^2 + 160 in^2 + 160 in^2 = 1,408 in^2.
Therefore, the correct answer is 1,408 in^2, which none of the options provided matches.
To find the surface area of a prism, you need to calculate the areas of all its faces and add them together.
In this case, we have a prism with a height (H) of 8in, a length (L) of 14in, and a width (W) of 10in.
The formula for the surface area of a rectangular prism is given by:
Surface Area = 2(LW + LH + WH)
Substituting the values into the formula, we get:
Surface Area = 2(14 * 10 + 14 * 8 + 10 * 8)
Surface Area = 2(140 + 112 + 80)
Surface Area = 2(332)
Surface Area = 664 in^2
Therefore, the correct answer is 664 in^2.