A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of ∠BAC∠BAC is four times that of ∠ACB∠ACB, and the height of the cylinder is equal to the diameter of its base, then the volume of the shaded region : Crackverbal Support

A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of ∠BAC∠BAC is four times that of ∠ACB∠ACB, and the height of the cylinder is equal to the diameter of its base, then the volume of th Print

Modified on: Tue, 12 Oct, 2021 at 2:00 PM

CONCEPT:The question discusses and applies the concepts of Mensuration and Geometry basics

SOLUTION:

Let us assume ∠ACB=x, therefore ∠BAC=4x,
∠ABC=x (△ABC is Isosceles with AC=AB (radii))

In triangle ABC,x+4x+x=180° , x= 30° ,
Thus, ∠BAC=4*30=120°

Volume is proportional to Cross sectional area(Circle for the entire cylinder and a sector for the shaded part).
This cross sectional area is proportional to angle which is 360 for the complete cylinder and
120 for the sector that represents the cross section area of the triangle.

Hence, Volume proportion of shaded region to entire Cylinder
= Angle of the sector/Angle of the full circle
=120/360 =1/3 (E)

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A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of ∠BAC∠BAC is four times that of ∠ACB∠ACB, and the height of the cylinder is equal to the diameter of its base, then the volume of th Print

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