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10 Jan 2021, 21:35
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C
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Difficulty:
45%
(medium)
Question Stats:
57% (01:27) correct
43%
(01:38)
wrong
based on 68
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A rectangle is rotated around one of its sides, creating a cylinder. What is the volume of the cylinder?
1) Circumference of the base of the cylinder is C
2) Diagonal of the rectangle is D
1) Circumference of the base of the cylinder is C
2) Diagonal of the rectangle is D
10 Jan 2021, 21:57
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The side about which it is rotated becomes the height of the cylinder, and the other side becomes the radius. You can imagine this by taking a cross section of the cylinder thus obtained.
Now its easy to get the two sides in terms of C and D and calculate the volume.
Now its easy to get the two sides in terms of C and D and calculate the volume.
10 Jan 2021, 22:58
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Let length of the rectangle be L and width be W
When rotated this cylinder about its length, width is the radius and length is height of the cylinder formed
Volume = pi * W^2 * L
1) Circumference of the base of the cylinder is C
C = 2*pi*W
W = C/2*pi
As L is unknown, volume cannot be calculated
Insufficient
2) Diagonal of the rectangle is D
D^2 = L^2 + W^2
Insufficient
(1)+(2);
D^2 = L^2 + W^2
L^2 = D^2 - W^2
Using W = C/2*pi in the above equation and calculating L, which is positive.
As L and W are know in terms of C and D, volume can be calculated
Sufficient
IMO C
When rotated this cylinder about its length, width is the radius and length is height of the cylinder formed
Volume = pi * W^2 * L
1) Circumference of the base of the cylinder is C
C = 2*pi*W
W = C/2*pi
As L is unknown, volume cannot be calculated
Insufficient
2) Diagonal of the rectangle is D
D^2 = L^2 + W^2
Insufficient
(1)+(2);
D^2 = L^2 + W^2
L^2 = D^2 - W^2
Using W = C/2*pi in the above equation and calculating L, which is positive.
As L and W are know in terms of C and D, volume can be calculated
Sufficient
IMO C
