Question

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

Answer 1

Heya Dear ☺

See The dimensions of the rectangular block or we can say a cuboid is 11dm×1m×5dm
here DM means decimeter

I know there will be a unit conversion doubt let me clear it out first

Mili
centi
deci
meter
deca
hecto
km
these are converted by 2 ways
if you wanna convert Milli to any down you need to divide 10 per unit
If you wanna convert km or any upper you need to multiply 10 per unit

Here we need to convert the dimensions in centi meter
so this will be like
$11 \times 10 = 110cm \\ 1 \times 100 = 100cm \\ 5 \times 10 = 50cm \\ since \: the \: dimensions \: of \: cuboid \: wil \: be \: \\ 110 \times 100 \times 50cm$
Now Given the radius of Bullet is 5 cm

To find:- Number of bullets

Solution:-
$volume \: of \: cuboid = l \times b \times h \\ 110 \times 100 \times 50$
Now
Radius = Half of the diameter
$volume \: of \: one \: bullet =\frac{4}{3}\pi \: r {}^{3} \\ \frac{4}{3} \times \frac{22}{7} \times \frac{5}{2} \times \frac{5}{2} \times \frac{5}{2}$

Number of bullets =
$\frac{volume \: of \: cuboid }{volume \: of \: one \: bullet } \\ \frac{110 \times 100 \times 50}{ \frac{4}{3} \times \frac{22}{7} \times \frac{5}{2} \times \frac{5}{2} \times \frac{5}{2}} \\ \\ 110 \times 100 \times 50 \times \frac{3}{4} \times \frac{7}{22} \times \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5}$
if you will cancel out
you will get the answer i.e

8400 Bullets

I hope it helped you
mark as brainliest

@mayankstar364

Answer 2

Answer:

The numbers of spherical bullets formed are 8400.

SOLUTION :

Given : Dimension of rectangular metallic block = 11dm × 1m × 5dm

and diameter of each  spherical  bullet = 5 cm

Dimension of rectangular metallic block = (11/10) m × 1m × (5/10)m = 1.1 m × 1 m × 0.5 m  

[1 dm = 1/10 m]

Radius of each  spherical  bullet =  5/2 cm = 2.5 cm = 2.5 /100 = 0.025 m = 25 × 10^-³ m

[1 cm = 1/100 m ]

Volume of rectangular metallic block = 1.1 m × 1 m × 0.5 m = 0.55 m³ = 55 × 10^-² m

Volume of rectangular metallic block = 55 × 10^-² m

Volume of the sphere =  4/3πr³

Volume of the sphere = 4/3 × 22/7 ×(25 × 10^-³ )³

Number of bullets  = Volume of the rectangular block / volume of the spherical bullets

= 55 × 10^-²  / 4/3 × 22/7 × (25 × 10^-³ )³

= 55 × 3 × 7 × 10^-²+^9 / 4 × 22×  25 × 25 × 25

= (3 × 7) × 10^7 / 8 × 5 × 625

= 21 × 10^7/ 40 × 625

= 21 × 10^7/ 25000

= 21 × 10^7/ 25 × 10³

= 21 × 10^7 × 10^-³ / 25

= 21 × 10⁴ / 25

= (21 × 10000)/25

= 21 ×  400

= 8400

Hence, the numbers of spherical bullets formed are 8400.

HOPE THIS ANSWER WILL HELP YOU...