If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area?
newarea = originalarea * (1/7)(1/7)(1/1)
A.
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B.
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C.
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D.
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It's D
To find the modified surface area of a rectangular prism when the width and height are each shrunk to one seventh of the original size while the length remains the same, we need to apply the formula for the surface area of a rectangular prism and adjust it accordingly.
The formula for the surface area of a rectangular prism is:
Surface Area = 2(length × width + length × height + width × height)
In this case, the length remains the same, but the width and height are reduced to one seventh of their original size. We can represent this as:
Modified Width = original width × (1/7)
Modified Height = original height × (1/7)
Now, we can substitute these modified dimensions into the surface area formula:
Modified Surface Area = 2(length × (original width × (1/7)) + length × (original height × (1/7)) + (original width × (1/7)) × (original height × (1/7)))
Simplifying this equation gives us the modified surface area formula:
Modified Surface Area = 2(length × width × (1/7) + length × height × (1/7) + width × height × (1/49))
So, the formula to find the modified surface area is:
Modified Surface Area = 2(length × width × (1/7) + length × height × (1/7) + width × height × (1/49))