3) The left and the right faces of a rectangular prism both have an area of 6 sq. cm, while the front and back faces both have an area of 8 sq. cm. If both have the base area of 12 sq. cm, what is the surface area of the cylinder?
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Answer:
ano ang tawag sa antas na naipapakita sa utang na loob
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Step-by-step explanation:
Let's start by labeling the dimensions of the rectangular prism.
Let the length be L, the width be W, and the height be H.
Fromthe problem, we know that the left and right faces both
have an area of 6 sq. cm. Since the base area is 12 sq. cm, we
can use this to solve for either L or H.
If we set the heightof the prism as H, we can use the formula
for the area of a rectangle (A =LxW) to find that the left face
has a length of 6/H and the right face also has a length of 6/
H
Similarly, since the front and back faces both have an area of
8 sq. cm and the base area is 12 sq. cm, we can use the same
formula to find that the front face has a length of 8/12H and
the back face also has a length of 8/12H.
Now that we know the dimensions of all four sides of the
prism, we can find the surface area by adding up the areas of
each face:
Surface area = 2lw+ 2lh + 2wh
Surface area = 2(6/H) (12/H) + 2(6/H) (H) + 2(12/H) (8/12H)
Surface area = 144H^2 +12 + 16/H
Surface area = (144 + 12H + 16)/H^2
Therefore, the surface area of the rectangular prism is (144 +
12H + 16)/H^2.