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How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, each bullet being 4 cm in diameter.

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2541

3521

2154

1545

answer is A.

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Detailed Solution

Let the number of spherical projectiles that can be made from a 44 cm cube of lead be n.
Now we find the value of the volume of spherical bullets with a diameter of 4 cm and a radius of 2 cm.
Volume of spherical bullets

= 43 π r 3

Volume of spherical bullets =

= 43 π (2) 3

= 43 π × 8 c m 3

= 43 × 227 × 8 c m 3 = 33.52 c m 3

So to calculate the volume of n number of spherical bullets of radius

2 c m

we will multiply it with n.
Volume of number of spherical bullets

= n × 33.52 c m 3 ...... (1)

Now, calculate the value of volume of cube of sides

44 c m = (44 c m) 3 = 85184 c m 3 ....... (2)

Now, equating equation (1) with equation (2) we get;

85184 c m 3 = n × 33.52 c m 3

Now, dividing 85184 by 33.52 we get;

⇒ n = 85184 c m 3 33.52 c m 3 = 2541.288 ≈ 2541

So the required number of spherical bullets that can be made out of a cube of metal is 2541.
So, the correct answer is Option 1.

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