How Many Spherical Bullets Each Of 5cm In Diameter Can Be Cast From A Rectangular Block Of Metal 11dm×1m×5dm?

We require the volume of the shapes while changing one shape into another. To determine the values, regular shapes have precise formulas. The volume of a form can be determined from its dimensions and vice versa. The length of one of the square's sides is all we need to determine its volume. We also need to know the radius of the sphere in order to calculate its volume. The volume of the original shape doesn't change when we change it into a new one.

Sphere

Every point on the sphere is the same distance from the center, making it a three-dimensional geometric shape. It has no edges whatsoever. Any point's constant distance from the center is called the sphere's radius.

The following is the formula for the sphere's volume:

Volume = \frac{4}{3}\pi r^{3}

Cube

A geometric object called a cube has 8 faces and 12 edges. The cube's face is square-shaped. The square's sides are of equal length.

The following is the formula for a cube's volume:

Let's write the cube's length as "a" to indicate it.

Volume = a^{3}

Given Information

Diameter of the bullet= 5cm

Rectangular block dimensions,

Length= 11dm

breath = 1m

height= 5dm

Solution

To find the number of bullets that can be cast from the block of metal, you need to determine each bullet's volume and divide the block's volume by the bullet's volume.

The formula gives the volume of each bullet for the volume of a sphere:

Volume = \frac{4}{3}\pi r^{3}

where r is the radius of the bullet.

The diameter of the bullet is 5 cm,

so the radius is 2.5 cm.

Plugging this value into the formula gives:

volume = \frac{4}{3}\pi (2.5)^3

\\= 1.33.. * 3.14 * 15.625

\\= 65.44 cm^3

The formula gives the volume of the block of metal for the volume of a cuboid:

volume = l * w * h

where l is the length, w is the width, and h is the height.

Since the dimensions of the block are given in decimeters (dm) and meters (m), you need to convert them to the same unit before you can calculate the volume.

1 meter is equal to 10 decimeters,

so the dimensions of the block in centimeters are:

l = 11 dm * 10 \frac{cm}{dm} = 110 cm

w = 1 m * 100 \frac{cm}{m} = 100 cm

h = 5 dm * 10 \frac{cm}{dm} = 50 cm

Plugging these values into the formula for the volume of a cuboid gives:

volume = 110 cm * 100 cm * 50 cm

\\= 55000 cm^3

Dividing the volume of the block by the volume of each bullet gives:

The number of bullets =\frac{ 55000 cm^3}{ 65.44 cm^3}

\\ = 839

Therefore, you can cast 839 spherical bullets from the block of metal.

Conclusion

839 spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11dm×1m×5dm.