SOLUTION: A square pyramid has a slant height of 25 m and a lateral area of 350^2 m. Which is the closest to the volume?

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Question 1180777: A square pyramid has a slant height of 25 m and a lateral area of 350^2 m. Which is the closest to the volume?
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
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No answer choices given....

The area of each of the four lateral faces is 350/4 = 175/2 square meters. With a slant height of 25m, the side length of the square base is 7m.

The foot of the altitude of the pyramid is in the center of the square base, 3.5m from each side of the base.

The height h of the pyramid can then be found as the length of the other leg of a right triangle with hypotenuse 25m and one leg 3.5m.

Then the volume of the pyramid is V=%281%2F3%29%287%5E2%29%28h%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A square pyramid has a slant height of 25 m and a lateral area of 350^2 m. Which is the closest to the volume?
given:
SA=350m%5E2
a slant height s=25m
The 350m%5E2 of lateral surface area is four congruent triangles, each with height 25m. If the side length of the square base is a, then
4%28a%2F2%29%2As=350
2a%2A25=350
a%2A50=350
a=350%2F50
a=7m
The side length of the square base is 7m.

The volume of a square pyramid is:
V+=+%281%2F3%29a%5E2%2Ah
h=sqrt%2825%5E2-%287%2F2%29%5E2%29
h=sqrt%282451%2F4%29
h=24.75

V+=+%281%2F3%29%287m%29%5E2%2A24.75m
V+=+404.25m%5E3