Question

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

Answer 1

Answer:

Step-by-step explanation

ROG

Answer 2

The number of spherical bullets is 8408

Step-by-step explanation:

Given as :

The diameter of spherical bullets = d = 5 cm

The radius of spherical bullets = r = $\dfrac{d}{2}$  

i.e                                                   r = $\dfrac{5}{2}$ = 2.5 cm = 0.025 m

The dimension of rectangular box =

Length = l = 11 d m =  1.1 m                      ( ∵ 1 m = 10 d m )

breadth = b = 1 m

height = h = 5 d m = 0.5 m

Let The number of spherical bullets = n

According to question

Volume of spherical bullet = V = $\dfrac{4}{3}$ × π × radius³

                                               V = $\dfrac{4}{3}$ × π × r³

Or,                                           V = $\dfrac{4}{3}$ × 3.14 × ( 0.025 m) ³

∴                                              V = 6.54167 × $10^{-5}$  cubic meter

So, The volume of spherical bullets = 6.54167 × $10^{-5}$  cubic meter

Again

The volume of rectangular box = v = length × breadth ×height

Or,                                                  v = l × b × h

Or,                                                  v = 1.1 m × 1 m × 0.5 m

∴                                                     v = 0.55 cubic meter

So, The volume of rectangular box = 0.55 cubic meter

Now,

Number of spherical bullets = $\dfrac{volume of rectangular box}{volume of spherical bullet}$

Or,                                         n = $\dfrac{v}{V}$

O,r                                        n = $\dfrac{0.55}{6.54167\times 10^{-5}}$

∴                                           n = 8407.6

So, The number of spherical bullets = n = 8408

Hence, The number of spherical bullets is 8408  Answer