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T6328.png
Circle P is the base of a right circular cone whose apex is D. Points A and B lie on circle P such that line segment AB is a diameter of P. If ADB is a right angle, and AD=32, then what is the volume of the cone?
A. 3
B. 6
C. 9
D. 18
E. 27
[Reveal] Spoiler:
The cone is a right cone, so AD=DB. Since ADB is a right angle, triangle ADB is a right isosceles triangle.
The ratio of the sides in a right isosceles triangle, a 45-45-90 triangle, is x:x:x2, so if the legs are of length 32, the hypotenuse AB, which is also the diameter of the base of the cone, is 32*2=3*2=6.
To calculate the height of the cone, connect points D and O. If radius OA is half of the diameter, or 3, and DA=32, then triangle DAO is also a right isosceles triangle. Thus, DO=OA=3.
Now you can find the volume of the cone: rh/3=9*3/3=9
The ratio of the sides in a right isosceles triangle, a 45-45-90 triangle, is x:x:x2, so if the legs are of length 32, the hypotenuse AB, which is also the diameter of the base of the cone, is 32*2=3*2=6.
To calculate the height of the cone, connect points D and O. If radius OA is half of the diameter, or 3, and DA=32, then triangle DAO is also a right isosceles triangle. Thus, DO=OA=3.
Now you can find the volume of the cone: rh/3=9*3/3=9
Attachment:
T1037816b.png