If the slant height of a right pyramid with square base is 4 meter and the total slant surface of the pyramid is 12 square meter, then what is the ratio of total slant surface and area of the base?Choices:- 16:3 24:3 9:7 12:3
Question
If the slant height of a right pyramid with square base is 4 meter and the total slant surface of the pyramid is 12 square meter, then what is the ratio of total slant surface and area of the base?Choices:- 16:3 24:3 9:7 12:3
Solution
The total slant surface area of the pyramid is given as 12 square meters. This is the sum of the areas of all the triangular faces of the pyramid.
For a pyramid with a square base, the slant height is the same for all faces. If the slant height is 4 meters, then each triangular face has an area of (1/2)baseheight = (1/2)base4.
Since the total slant surface area is 12 square meters, and there are 4 triangular faces, each face must therefore have an area of 12/4 = 3 square meters.
So, the base of each triangle (which is also a side of the square base of the pyramid) must be 2Area/height = 23/4 = 1.5 meters.
The area of the square base of the pyramid is then base^2 = 1.5^2 = 2.25 square meters.
The ratio of the total slant surface to the area of the base is then 12/2.25 = 16/3.
So, the answer is 16:3.
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