SOLUTION: Maria built a wooden storage shed in the shape of a cube with sides 12 feet on each side capped by a right square pyramid, as shown in the figure below. The height of the entire fi
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Question 747026: Maria built a wooden storage shed in the shape of a cube with sides 12 feet on each side capped by a right square pyramid, as shown in the figure below. The height of the entire figure is 20 feet. Maria needs to paint all of the lateral surfaces of the shed, including the roof but not including the floor. What is the surface area that will need to be painted?
http://ed.edim.co/18995163/pic332.jpg?Expires=1368144532&Signature=B2Y~GZSUppEZw39ToJJCZg5xBzEitr1rIBscN32CSlHMjWrQO-R~IhP4GBp22W7NnOD2kQdLDVMw~c~PiLk0XlCulh5dyIVHNP4pWc2vSItFryl00iQyjNs6sJjD6o5jpeuJuvRJ1E6xOI5dpJMR9NEr3pJM9kG~WRGiGsMGgvM_&Key-Pair-Id=APKAJI74L7OXO7CNJA7Q Answer by MathLover1(20850) (Show Source):
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the lateral surface area of a regular pyramid is L.S.A where represents the perimeter of the base and the slant height
where = length of the side
Maria needs to paint all of the lateral surfaces of the shed, including the roof but not including the floor:
so, she will need L.S.A and since she doesn’t need bottom and top of cube (both are inside shed)
L.S.A ... and the slant height will be hypothenuse of right triangle formed by the hight of pyramid and half of the side length of the base
L.S.A
L.S.A
L.S.A
and
so, total surface area is:
