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07 Dec 2020, 01:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:31) correct
25%
(02:48)
wrong
based on 63
sessions
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The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?
A. \(729-162\pi\)
B. \(729-\frac{81\pi}{2}\)
C. \(729-81\pi\)
D. \(729-9\pi\)
E. \(729\)
Attachment:
1.jpg [ 18.01 KiB | Viewed 3424 times ]
07 Dec 2020, 05:10
Kudos
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Explanation:
Diagonal AB = Side of Cube x √2 = 9√2
Diameter of Cylinder = 9√2/3 = 3√2 , r = 3√2/2
Area of Cylinder CD = π*r^2*h = π*(3√2/2)^2*9 = π*9x2x9/4 = 81π/2
Area of Cube = (side)^3 = 9^3 = 729
Resultant area = 729 - 81π/2
IMO-B
Diagonal AB = Side of Cube x √2 = 9√2
Diameter of Cylinder = 9√2/3 = 3√2 , r = 3√2/2
Area of Cylinder CD = π*r^2*h = π*(3√2/2)^2*9 = π*9x2x9/4 = 81π/2
Area of Cube = (side)^3 = 9^3 = 729
Resultant area = 729 - 81π/2
IMO-B
07 Dec 2020, 11:15
Kudos
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IMO answer B
Diagonal AB = 9√2
=> Diameter Cylinder = 9√2/3 = 3√2
=> radius = 3/√2
=> Area of Cylinder CD = π*r^2*h = π*((3/√2)^2)*9 = π*9x2x9/4 = 81π/2
Required area = 729 - 81π/2
Diagonal AB = 9√2
=> Diameter Cylinder = 9√2/3 = 3√2
=> radius = 3/√2
=> Area of Cylinder CD = π*r^2*h = π*((3/√2)^2)*9 = π*9x2x9/4 = 81π/2
Required area = 729 - 81π/2
Bunuel
