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24 Jun 2021, 09:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:35) correct
35%
(01:34)
wrong
based on 20
sessions
History
Date
Time
Result
Not Attempted Yet
Find the number of spherical balls, each of diameters 1 mm that can be made from a solid sphere of radius 4 cm.
(A) 512
(B) 5120
(C) 25600
(D) 51200
(E) 512000
(A) 512
(B) 5120
(C) 25600
(D) 51200
(E) 512000
24 Jun 2021, 09:20
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Explanation:
No. Of spherical balls = 40x40x40/0.5x0.5x0.5
= 64000/0.125
= 51200
IMO-E
Posted from my mobile device
No. Of spherical balls = 40x40x40/0.5x0.5x0.5
= 64000/0.125
= 51200
IMO-E
Posted from my mobile device
24 Jun 2021, 09:22
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Bunuel
number of smaller balls = \((\frac{R}{r})^3\)
= \((\frac{4}{1/2})^3\)
= \((2^2*2)^3\)
= \(2^9\)
= 512
The units are different so it has to be equated. Bigger sphere volume is \(10^3 mm^3\) times bigger than smaller sphere. Hence
number = 512 * 1000 = 512000
Answer E.
