Question

How many spherical bullets can be made out of a solid cube of lead whose edge measures 66 cm each bullet being 6 cm in diameter?

Answer 1

2541 bullets can be made from the cube...

Answer 2

Given,

• Edge of the solid cube = 66 cm
• Diameter of the bullet = 6 cm

To find,

• The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 66 cm each bullet being 6 cm in diameter.

Solution,

The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 66 cm each bullet being 6 cm in diameter is 2541.

We can simply find the number of spherical bullets that can be made out of a solid cube of lead whose edge measures 66 cm each bullet being 6 cm in diameter by using the following fact

The volume of the n spherical bullets of diameter 6 cm = volume of the solid cube of edge 66 cm

As we know,

The volume of sphere = 4/3 πr³

Diameter of the spherical bullet = 6 cm

Radius = diameter /2        

Radius of the spherical bullets = 6/2

                                                   = 3 cm

The volume of one spherical bullet = 4/3* π * (3)³         (1)

The volume of the cube = (side)³

The volume of the solid cube = (66)³                              (2)

Number of spherical bullets = Volume of the solid cube of lead / Volume of one spherical bullet

                                                 = $66 * 66 * 66 / 4/3 * 22/7 * 3 * 3 * 3$

                                                 = $66 * 66 * 66 * 21 / 4 * 22 * 3* 3*3$

                                                 = $22 * 22 *21 / 4$

                                                 = $121*21$

                                                 = $2541$

Hence, the number of spherical bullets that can be made out of a solid cube of lead whose edge measures 66 cm each bullet being 6 cm in diameter is 2541.