If the length of each dimension of the rectangular prism is cut in half, then surface area will be 1/4 of the original surface area. true or false
True , the surface area of similar objects is proportional to the square of the sides
(1/2)^2 = 1/4
true
bad no no is bad a no
To determine whether the given statement is true or false, let's break it down and analyze it step by step.
The surface area of a rectangular prism can be calculated by finding the sum of the areas of all six faces. The formula for calculating the surface area of a rectangular prism is:
Surface Area = 2(ab + ac + bc)
where 'a', 'b', and 'c' represent the lengths of three different dimensions of the rectangular prism.
Now, according to the statement, if each dimension is cut in half, we have new dimensions of (a/2), (b/2), and (c/2).
Substituting these new dimensions into the surface area formula, we get:
New Surface Area = 2((a/2)(b/2) + (a/2)(c/2) + (b/2)(c/2))
Simplifying this expression:
New Surface Area = (ab/4) + (ac/4) + (bc/4)
Combining the terms with common denominators, we get:
New Surface Area = (ab + ac + bc)/4
Comparing the new surface area with the original surface area, we have:
New Surface Area = (ab + ac + bc)/4
Original Surface Area = 2(ab + ac + bc)
Dividing the new surface area by the original surface area, we get:
(New Surface Area)/(Original Surface Area) = [(ab + ac + bc)/4] / [2(ab + ac + bc)]
Simplifying this expression:
(New Surface Area)/(Original Surface Area) = 1/8
Therefore, we can conclude that the new surface area, when each dimension is cut in half, is 1/8 times the original surface area.
Hence, the given statement "If the length of each dimension of the rectangular prism is cut in half, then surface area will be 1/4 of the original surface area" is false. The correct statement should be "If the length of each dimension of the rectangular prism is cut in half, then surface area will be 1/8 of the original surface area."