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23 Jul 2023, 01:54
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85%
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Question Stats:
27% (01:40) correct
73%
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based on 33
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A right circular cone is cut (parallel to base) into 7 slides of the same height. What is the ratio of curved surface area of the middle slice to that of the largest slice?
A. 3:4
B. 4:7
C. 7:13
D. 16:49
E. 4:11
from unacademy
A. 3:4
B. 4:7
C. 7:13
D. 16:49
E. 4:11
from unacademy
26 Jul 2023, 14:39
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Imagine the cone in 3D with 7 sections cut out. We have 7 radii running parallel. Similarity of triangles give us r1/l1 = r2/l2=r4/l4= r4/l5= k.
Further, for these triangles, l1=height= 7L, l2= 6L, l4=4L, l5=3L etc.
Curved surface area if frustum is pi*height*(r + r'). Of which height is constant/gets cancelled out.
So, A1/A2 = (7Lk + 6Lk)/(4Lk + 3Lk) = 13/7.
Further, for these triangles, l1=height= 7L, l2= 6L, l4=4L, l5=3L etc.
Curved surface area if frustum is pi*height*(r + r'). Of which height is constant/gets cancelled out.
So, A1/A2 = (7Lk + 6Lk)/(4Lk + 3Lk) = 13/7.
18 Aug 2023, 22:54
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let height of right circular cone be 7h, radius be 7r, slant height be 7s. cutting into 7 equal parts wrt height will mean nth part from top will have height n*h, radius n*r, slant height n*s. middle slice will be n=4 from top. largest slice will n=7 from top. Note that Curved surface area (CSA) of right circular cone = pi*radius*(slant height)
In our case, CSA of n-th slice is CSA of cone considering n slices - CSA of cone considering (n-1) slices. So, CSA of middle slice = pi*4r*4s - pi*3r*3s = 7*pi*r*s. Similarly CSA of largest slice is pi*r*s*(7*7 - 6*6) = 13*pi*r*s. so the ratio is 7:13
In our case, CSA of n-th slice is CSA of cone considering n slices - CSA of cone considering (n-1) slices. So, CSA of middle slice = pi*4r*4s - pi*3r*3s = 7*pi*r*s. Similarly CSA of largest slice is pi*r*s*(7*7 - 6*6) = 13*pi*r*s. so the ratio is 7:13
