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To find if the surface area of the first pyramid is one third of the surface area of the second pyramid.
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Answer to Problem 41E
The surface area of pyramid 2 is greater than pyramid 1, but not by 3 times.
Explanation of Solution
Given information:
Two pyramids have congruent bases.
The slant height of the first pyramid is one-third of the slant height of the second pyramid.
Formula used:
Surface area of pyramid,
Let l=x , where l is slant lenght
where s is square base side
where B is the base area where P is perimeter of base
For pyramid 1:
Assuming pyramid is square, Base area B and perimeter P will be,
Substituting value of B and P in surface area formula,
On solving,
.........(1)
For pyramid 2:
Assuming pyramid is square, Base area B and perimeter P will be,
Here, slant lenght is l=3x given in question.
Substituting value of B , P and l in surface area formula,
On solving,
.......(2)
On comparing equation (1)and(2),
SA of pyramid 2 is greater than SA of pyramid 1,but not 3 times.
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