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06 May 2020, 04:03
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:56) correct
53%
(03:26)
wrong
based on 47
sessions
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A sphere of radius 14 cm is cut by a plane at a distance of x cm from its center, thereby breaking this sphere into two different pieces. If the cumulative surface area of these two pieces is 3/28 times more than that of the sphere, what is the value of x ? (The surface area of a sphere = 4πr^2)
A. 10.4
B. 11.4
C. 12.4
D. 12.5
E. 13
Are You Up For the Challenge: 700 Level Questions
A. 10.4
B. 11.4
C. 12.4
D. 12.5
E. 13
Are You Up For the Challenge: 700 Level Questions
yashikaaggarwal
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Joined: 19 Jan 2020
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06 May 2020, 05:01
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Closest answer in approximate value is C
Distance of X from centre is r= √(R^2-x^2)
The CSA of two pieces of square is equal to the 3/28 time more than the surface area of sphere
4πR^2+2πr^2=3/28 time more than the surface area of sphere.
4π14^2+2π√(R^2-x^2)^2=3/28
2464+2*22/7(14^2-x^2)=2728
X^2=154
X=12.4
OA is C
Posted from my mobile device
Distance of X from centre is r= √(R^2-x^2)
The CSA of two pieces of square is equal to the 3/28 time more than the surface area of sphere
4πR^2+2πr^2=3/28 time more than the surface area of sphere.
4π14^2+2π√(R^2-x^2)^2=3/28
2464+2*22/7(14^2-x^2)=2728
X^2=154
X=12.4
OA is C
Posted from my mobile device
06 May 2020, 05:09
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Bunuel
Solutions
- • radius of the sphere, \(r = 14cms\)
• So total surface area of the sphere \(= 4*\pi*r^2 = 4*\pi*14^2\)
• Now, the sphere is at cut by a plane at a distance x. Cutting of the sphere by a plane in two pieces will exposes two new circular surfaces, which will be identical. (shown in the below figure).
• From the above figure, we can write, radius of each circular surface \(= \sqrt{14^2 – x^2}\)
• Now the increase the cumulative surface area of these two faces will only be contributed by these two identical circular faces.
- o Therefore, \(2*\pi*(14^2 – x^2) = \frac{3}{28}*4*\pi*14^2 ⟹ 14^2 – x^2 = 42 ⟹x^2 =196 – 42 ⟹ x^2 = 154\)
- o So, we can eliminate answer Options A, B and E.
- o Option D: 12.5
- \(12.5 = \frac{25}{2 }⟹(12.5)^2 = \frac{625}{4} = 156.25\)
- \(12.4 = \frac{124}{10} ⟹12.4^2 = (\frac{124}{10})^2 = \frac{15376}{100} = 153.76\)
This value is closer to 154 than the Option D (i.e. 156.25)
