Spherical bullets can be made out of a solid lead cube whose edge measures 33 cm. Each bullet has a

M4maths Previous Puzzles

26 Nov 2015 Volume

Spherical bullets can be made out of a solid lead cube whose edge measures 33 cm. Each bullet has a radius of 1.5 cm and is required to be covered by another material of thickness 2mm. Find the volume of material required.

OPtion

1) 16776.72 cm^3
2) 15366.42 cm^3
3) 18576.12 cm^3
4) 16376.62 cm^3
5) 12346.82 cm^3
6) 14372.44 cm^3
7) 12444.66 cm^3
8) 16678.56 cm^3
9) 16736.26 cm^3
10)None of these

Solution

We have
cube edge length a = 33 cm
r = 1.5 cm
Volume of one bullet = 4/3 Pi r^3
= 4/3 *22/7 * (3/2)^3 = 11/7 * 9
Volume of cube = a^3 = 33^3
Let the number of bullets that can be made be n
n = Volume of cube / volume of one bullet
= 33*33*33/ (99/7) = 11*33*7 = 2541
So 2541 bullet can be made
Volume of material required = 2541*(4*Pi/3 (1.5+0.2)^3 - 4*Pi/3(1.5)^3)
= 16376.62 cm^3

Correct Option: 4 Best Solution (6)

Pooja Shaw   9 years AGO

edge of the cube=33 cm
vol of the cube=33^3 cm^3=35937 cm^3
radius of bullet=1.5 cm
vol of bullet=4/3*pi*(1.5)^3 cm^3=297/21 cm^3
radius of bullet with outer layer=1.7cm
vol of bullet with outer layer=4/3*pi*1.7^3 cm^3
=432.344/21
therefore,volume of the material=432.344/21-297/21
lets no of bullets is n
therefore,n*297/21=35937
solving this we get n=2541
therefore,volume of material in 2541 bullets=2541(432.344/21-297/21)=16376.62 cm^3
Thus correct answer is 4)

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Vinay Sipani    9 years AGO

volume of cube = 33^3 = 35937 cm^3
Volume of 1 bullet = (4/3)*pi*1.5^3 = 9*pi/2 cm^3
=> Number of bullets = 35937/(9*pi/2) = 2542

Volume of 1 material over bullet = (4/3)*pi*(1.7^3 - 1.5^3) = 769*pi/375 = x

=> Volume of material = 2542 * x
= 16376.42
=> option 4

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harshavi   9 years AGO

the volume of cube=33^3
the volume of spheres made =n*4*3.14*(1.5)^3
both are equal
thus we get n=2541(no of bullets that can be made)
thus for each bullet the volume of materail required is
4*3.14*((1.7)^3-(1.5)^3)/3=6.445cu.cm
thus for 2541 bullets we require 2541*6.445=16376.62 cm^3

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anand modi   9 years AGO

BY VOLUME CONSERVATION,
SUPPOSE N = NUMBER OF BULLET FORMED,
SO,
33^3 =N*(4/3)*3.1415*(1.5)^3,
AFTER SOLVING
N=2524,
THEREFORE VOLUME REQUIRED=N*(4/3)*3.1415*(1.7^3-1.5^3),
16376.62cm^3
option 4)

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bhaskar   9 years AGO

(33*33*33/(4*pi*1.5*1.5*1.5/3))*(4*pi(1.7*1.7*1.7-1.5*1.5*1.5)/3)=16376.62

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anjali gupta   9 years AGO

vol of cube=33*33*33=35937 cm^3
vol of sphere= 4*22*(1.5)^3/(3*7) cm^3
no. of sphere= vol of cube/vol of sphere=2541
vol of material around sphere= 2541*(4/3)(22/7)(1.7^3-1.5^3) cm^3
=16376.62 cm^3

Like? Yes (1) | No