SOLUTION: Find the total cost of polishing , if it cost 10 php per square meter to polish the lateral surface area of a 10 meter marble monument in the shape of a frustum of a regular pyrami

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Question 1025449: Find the total cost of polishing , if it cost 10 php per square meter to polish the lateral surface area of a 10 meter marble monument in the shape of a frustum of a regular pyramid with upper and lower base edges measuring 8 m and 4 m, respectively.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
All length measurements will be in meters, and all surface area measurements will be in square meters, but I will not write the units except at the end.
The cross-section of that pyramid and frustum would look like this:
with similar triangles
The large right triangle has the same angle measures,
and twice the base (4 rather than 2), compared to the smaller right triangle.
So, the height of the large right triangle is twice the height of the smaller one,
meaning that the height of the frustrum (10) and the height of the small triangle are both half of the height of the large triangle ( 2%2A10=20 ).

In the large right triangle, the Pythagorean theorem says that
%282x%29%5E2=4%5E2%2B20%5E2
%282x%29%5E2=16%2B400
%282x%29%5E2=416
2x=sqrt%28416%29 is the slant height of the pyramid.
The lateral faces of pyramid and frustrum look like this:
and
The surface area of each of the lateral faces of the frustum can be calculated as
%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29
The total lateral surface area can be calculated as
4%2A%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29=12sqrt%28416%29 .
At 10 php per square meter, the cost for polishing the lateral surface would be
10%2A12%2Asqrt%28416%29=%22approx.%22highlight%28247.53php%29 .