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05 May 2020, 10:48
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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Question Stats:
81% (02:05) correct
19%
(03:09)
wrong
based on 53
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Red ribbon string is put around two circular disks as shown above. If the radii of the two disks are 40 cm and 30 cm, respectively, what is the total length of the string?
A. \(140\) cm
B. \(140 + \frac{165π}{2}\) cm
C. \(140 + 105π\) cm
D. \(140 + 120π\) cm
E. \(140 + 165π\) cm
Attachment:
Untitled.png [ 5.57 KiB | Viewed 2595 times ]
05 May 2020, 11:08
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Bunuel
Given: Red ribbon string is put around two circular disk as shown above.
Asked: If the radii of the two disk are 40 cm and 30 cm, respectively, what is the total length of the string?
Total length of string = 270/360 * 2π *(30 + 40) + 2*(40+30) = 70 (3π/2 + 2) = 140 + 105π
IMO C
06 May 2020, 03:11
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*********************************
So, Since the ribbon covers 3/4th of the ribbon, use the formula:
3/4( 2 Pi R)
So, you would have 3/4(2*Pi* 40) = 3/4(2*Pi*30)
which will equal to 105 Pi. -----1
Keeping that aside, let's work on the intersecting tangential lines.
we know that three angles in the respective quadrilaterals are 90. so, the fourth angle also should be 90.
which makes all the sides equal(as the radius of a circle is equal at any point on the circumference).
for tangent 1, we will get (40+30) = 70
similarly, for tangent 2, we will get (30+40) = 70 -----2
Hence, by 1&2, we will get 140+ 105Pi
So, Since the ribbon covers 3/4th of the ribbon, use the formula:
3/4( 2 Pi R)
So, you would have 3/4(2*Pi* 40) = 3/4(2*Pi*30)
which will equal to 105 Pi. -----1
Keeping that aside, let's work on the intersecting tangential lines.
we know that three angles in the respective quadrilaterals are 90. so, the fourth angle also should be 90.
which makes all the sides equal(as the radius of a circle is equal at any point on the circumference).
for tangent 1, we will get (40+30) = 70
similarly, for tangent 2, we will get (30+40) = 70 -----2
Hence, by 1&2, we will get 140+ 105Pi
