the castle is in the shape of a rectangular prism. the length is 25 feet long 157 feet wide. the height of the castle measures 38 feet. what is the surface area of the castle? what is the volume of the castle?
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To find the surface area of a rectangular prism, we need to add up the areas of all six faces. The formula for the surface area of a rectangular prism is:
Surface Area = 2ab + 2bc + 2ac
where a, b, and c are the dimensions of the rectangular prism.
In this case, the length (l) is 25 feet, the width (w) is 157 feet, and the height (h) is 38 feet. Let's substitute these values into the formula:
Surface Area = 2lw + 2wh + 2lh
Surface Area = 2(25)(157) + 2(157)(38) + 2(25)(38)
To calculate this, we can multiply each value accordingly:
Surface Area = 2(3925) + 2(5974) + 2(950)
Surface Area = 7850 + 11948 + 1900
Surface Area = 21698 square feet
Therefore, the surface area of the castle is 21,698 square feet.
Now, to find the volume of the rectangular prism, we need to multiply the length, width, and height. The formula for the volume of a rectangular prism is:
Volume = length x width x height
Substituting the given values:
Volume = 25 x 157 x 38
Volume = 117,850 cubic feet
Therefore, the volume of the castle is 117,850 cubic feet.