Question

How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11 diameter into 1m into 5 diameter?

Answer 1

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Answer 2

Answer:

The number of bullets are 8400.

Step-by-step explanation:

Given : The total number of spherical bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of a rectangular block of lead with 11 metre length 10 metre breadth and 5 metre width.

To find : The number of bullets used?

Solution :

Dimension of a rectangular box is

l=11 m, b=10 m, h=5 m

Volume of the rectangular box is

$V_b=l\times b\times h$

$V_b=11\times 10\times 5$

$V_b=550m^3$

Convert into decimeter,

$V=550\times 1000=550000dm^3$

Dimension of the bullet,

Diameter = 5 dm , Radius = 5/2 dm.

Volume of the sphere is

$V_s=\frac{4}{3}\pi r^3$

$V_s=\frac{4}{3}\times \frac{22}{7}\times \frac{5}{2}\times \frac{5}{2}\times \frac{5}{2}$

$V_s=65.47dm^3$

Number of bullets is volume of box divided by volume of sphere.

$n=\frac{V_b}{V_s}$

$n=\frac{550000}{65.47}$

$n=8400.7$

Approximately The number of bullets are 8400.