How Many Shots Each Having A Diameter Of 3 Cm Can Be Made From A Cuboidal Lead Solid Of Dimensions 9cm × 11cm?

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 at 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/Cuboid

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. A cuboid has rectangular faces.

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}

For a cuboid, formula for volume of a cuboid is given as

Where, l, w and h represent length, width and height respectively.

Given Informations

The Diameter of the shots= 3cm

The dimensions of the cuboidal lead solid are as follows:

Length= 9cm

Width= 11cm

height= 12cm

Solution

To find the number of shots that can be made from the lead solid ( cuboid), we need to determine the volume of each shot and then later divide the volume of the lead solid (cuboid) by the volume of the shot.

The formula given below gives the volume of each shot for the volume of a sphere:

Volume = \frac{4}{3}\pi r^{3}, where r is the radius of the shot.

As given in the question above,

The diameter of the shot is 3 cm,

So therefore the radius is = \frac{3}{2}= 1.5 cm

.

The pie value is taken as 3.14 and can also be taken as 22/7 still the answer remains the same.

Plugging this value into the formula gives:

volume = \frac{4}{3}\pi (1.5)^3

\\= 1.33.. * 3.14 * 3.375

\\= 7.07 cm^3

Therefore the volume of each shot for the volume of a sphere is, 7.07 cm^3

The formula gives the volume of the lead solid for the volume of a cuboid:

volume = l * w * h

where l is the length,

w is the width, and

h is the height.

Plugging in the values given in the problem gives:

volume = 9 cm * 11 cm * 12 cm

\\= 1188 cm^3

Therefore the volume of the lead solid for the volume of a cuboid is, 1188 cm^3

Dividing the volume of the lead solid ( cuboid ) by the volume of each shot gives:

The number of shots = \frac{1188^3}{7.07^3}

\\ = 167.5

Since you can't have a fraction of a shot,

You can only make 167 shots from the lead solid.

Conclusion

167 Shots Each Having A Diameter Of 3 Cm Can Be Made From A Cuboidal Lead Solid Of Dimensions 9cm × 11cm × 12cm?