A right pyramid on a base10m square is 15m high find the volume of the pyramid if the top 6m of the pyramid are removed what is the volume of the remaining frustum
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To find the volume of the pyramid, we can use the formula:
Volume of a pyramid = (1/3) * base area * height
The base of the pyramid is a square with side length 10m, so the base area is:
Base area = 10m * 10m = 100m^2
The height of the pyramid is 15m.
Using the formula, we can calculate the volume of the original pyramid:
Volume of the original pyramid = (1/3) * 100m^2 * 15m
Volume of the original pyramid = 500m^3
Now, let's find the volume of the remaining frustum after removing the top 6m of the pyramid.
The height of the remaining frustum can be calculated by subtracting 6m from the original height:
Height of the remaining frustum = 15m - 6m = 9m
The remaining frustum has the same base as the original pyramid, with a base area of 100m^2.
Using the formula, we can calculate the volume of the remaining frustum:
Volume of the remaining frustum = (1/3) * 100m^2 * 9m
Volume of the remaining frustum = 300m^3
Therefore, the volume of the remaining frustum after removing the top 6m of the pyramid is 300 cubic meters.
volume = 1/3 * area of base * height
vol top 6 m = 1/3 * [(6/15) * 10]^2 * 6