The area of the base of the truncated cone is 4dm2 and 16dm2 through the middle of the height

univerkov | April 2, 2021 | education

The area of the base of the truncated cone is 4dm2 and 16dm2 through the middle of the height, a plane is drawn parallel to the bases. Find the cross-sectional area.

Knowing the area of the base of the truncated cone, we determine the radii of its bases.

S1 = π * AD ^ 2 = 16 dm2.

AD = √16 / π = 4 / √π dm.

S1 = π * ВС ^ 2 = 4 dm2.

ВС = √16 / π = 2 / √π dm.

The quadrilateral ABCD is a rectangular trapezoid, since BC is parallel to AD, and CD is perpendicular to AD and BC.

Point O, by condition, is the middle of CD, then the segment OK is the middle line of the trapezoid.

OK = (BC + AD) / 2 = (2 / √π + 4 / √π) / 2 = 3 / √π dm.

Then the cross-sectional area is equal to:

Ssection = π * KO ^ 2 = π * 9 / π = 9 dm2.

Answer: The cross-sectional area is 9 dm2.

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