Question

How many spherical bullets, each 5 dm in diameter can be cast from a rectangular block of lead $11 m \times 10 m \times 5 m$? $(\pi = \dfrac{{22}}{7})$.

Answer 1

Hint: In the above question we have the diameter of a spherical bullet and length, width, and height of the rectangular block. To find the number of spherical bullets that can be cast from a rectangular block of lead then we have to find the volume of the spherical bullet and the volume of the rectangular block of lead. Then finally we will divide the Volume of the Rectangular block of lead with the volume of the spherical bullet.

Complete step by step solution:
Given,
Diameter of spherical bullets = 5 dm
Radius of spherical bullet = $\dfrac{5}{2}$ dm [$\text{Diameter} = 2 \times \text{Radius}$]
Volume of a spherical bullet $ = \dfrac{4}{3}\pi {r^3}$
where r is the radius of the sphere.
Volume of spherical bullet
$ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times \dfrac{5}{2} \times \dfrac{5}{2} \times \dfrac{5}{2}$
$ = \dfrac{{1375}}{{21}}d{m^3}$
Now, the length of rectangular block of lead = 11 m
The width of rectangular block of lead = 10 m
The height of rectangular block of lead = 5 m
Volume of rectangular block of lead = length × breadth × height
$ = 11 \times 10 \times 5 = 550{m^3}$
$ = 550 \times 1000 = 550000d{m^3}$(1 m = 10 dm)
Number of spherical bullets can be cast from a rectangular block of lead $ = \dfrac{{550000}}{{\dfrac{{1375}}{{21}}}} = \dfrac{{550000 \times 21}}{{1375}} = 8400$bullets

$\therefore $ The number of spherical bullets can be cast from a rectangular block of lead is 8400 bullets.

Note:
A sphere is a three-dimensional object. It is round in shape like a ball. In these types of question, always use the concept of volume conversion i.e. volume of an object remains unchanged when converted to another shape. And to find the number of spherical bullets as in this question, use unitary method. You must remember formulas of volumes of some basic three-dimensional objects.