Question

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

Answer 1

Answer:

Number of bullets = 8400.

Step-by-step explanation:

Given : Spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11 dm*1 m*5 dm.

To find : How many spherical bullets were there ?

Solution :

First we convert the dimensions into one dimension i.e, cm,

$11 \times10= 110cm \\ 1 \times 100 = 100cm \\ 5 \times 10 = 50cm$

So, The dimensions of the cuboid is $110 \times 100 \times 50cm$

The volume of the cuboid is

$V=110 \times 100 \times 50cm$

Now we have given the diameter of Bullet is 5 cm.

Radius $r=\frac{5}{2}cm$

Volume of the bullet is

$v=\frac{4}{3}\pi r^3$

$v=\frac{4}{3}\frac{22}{7}(\frac{5}{2})^3$

$\text{Number of bullets} = \frac{\text{volume of cuboid}}{\text{volume of one bullet}}$

$\text{Number of bullets} =\frac{110 \times 100 \times 50}{ \frac{4}{3}\times \frac{22}{7} \times\frac{5}{2} \times\frac{5}{2} \times\frac{5}{2}}$

$\text{Number of bullets} =110\times 100\times 50 \times\frac{3}{4} \times\frac{7}{22}\times\frac{2}{5}\times\frac{2}{5} \times\frac{2}{5}$

$\text{Number of bullets} =8400$

Therefore, Number of bullets = 8400.

Answer 2

Answer:

8400

Step-by-step explanation:

11×10=110cm

1×100=100cm

5×10=50cm

So, The dimensions of the cuboid is 110 \times 100 \times 50cm110×100×50cm

The volume of the cuboid is

V=110 \times 100 \times 50cmV=110×100×50cm

Now we have given the diameter of Bullet is 5 cm.

Radius r=\frac{5}{2}cmr=

2

5

cm

Volume of the bullet is

v=\frac{4}{3}\pi r^3v=

3

4

πr

3

v=\frac{4}{3}\frac{22}{7}(\frac{5}{2})^3v=

3

4

7

22

(

2

5

)

3

\text{Number of bullets} = \frac{\text{volume of cuboid}}{\text{volume of one bullet}}Number of bullets=

volume of one bullet

volume of cuboid

\text{Number of bullets} =\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}}Number of bullets=

3

4

×

7

22

×

2

5

×

2

5

×

2

5

110×100×50

\text{Number of bullets} =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}Number of bullets=110×100×50×

4

3

×

22

7

×

5

2

×

5

2

×

5

2

\text{Number of bullets} =8400Number of bullets=8400

Therefore, Number of bullets = 8400.