A cone, placed on a table, is cut from the middle by a horizontal plane. The lower portion is placed

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23 Oct 2015 Visible Area

A cone, placed on a table, is cut from the middle by a horizontal plane. The lower portion is placed in inverted position & upper portion is placed symmetrically on it. Calculate the total visible area (Take R = 14 cm, Pi = 22/7 and h = 48cm)

OPtion

1) 2472 cm^2
2) 2664 cm^2
3) 2642 cm^2
4) 2564 cm^2
5) 2482 cm^2
6) 2364 cm^2
7) 2662 cm^2
8) 2766 cm^2
9) 2854 cm^2
10)None of these

Solution

Total visible are = surface are of cone + surface are of frustum + area of the ring

Using figure and solve it
Area = 2662 cm^2

Correct Option: 7 Best Solution (4)

anushka bansal   9 years AGO

total surface area of cone + (area of base of the original cone - area of base of the smaller cone)
slant height s = sqrt(48^2+14^2)
= 50
total surface area = pi*r*s = 22/7*14*50 = 2200
visible area = 2200 + (pi*14*14 - pi*7*7)
2662cm^2

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ABHISHEK GAURAV   9 years AGO

As it is clearly mentioned in the question is that the cone is cut horizontally in the middle such that its height gets halved.
Area of the upper most cone is = pi*r(r+sqrt(h^2+r^2))
(as the lower portion of the cone is not visible, so we will not take the value of r in the formula)
= 22/7*7( sqrt(24^2+7^2)
=550cm^2
area of concentric circle around the cone=pi(14^2-7^2)
= 462cm^2
area of lower part of the cone=
pi*r(sqrt(14^2+48^2)) - pi* 7 (7^2+24^2)
= 1650cm^2

adding all these areas= 550+462+1650
= 2662 cm^2

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vikash ranjan   9 years AGO

22/7 *14 (48*48 +14*14)^1/2 + 22/7 (14*14 - 7*7 )= 2662

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RAKESH   9 years AGO

R=14, r=7, L=l=25

pi(R+r)L + pi*rl + pi(R^2-r^2) ===== 2662 cm^2

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