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Find the total area of the frustum of a regular square pyramid which is inscribed
in the frustum of a cone whose upper and lower base diameters are 11 ft and 15 ft
respectively, and whose altitude is 19 ft.
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Use the formula for the volume of a regular pyramidal frustum
V = ,
where h is the height, and are the base areas
(see this source https://mathworld.wolfram.com/PyramidalFrustum.html) .
In your case, the bases are the squares with their diagonals 11 ft and 15 ft.
Their areas are square feet and square feet, respectively;
h = 19 ft. Therefore, the volume of the frustum is
V = = =
= = = = 1618.167 cubic feet (rounded).
ANSWER. The volume is = 1618.167 cubic feet (rounded).
Solved.