Question

a cylindrical jar of diameter 14cm and depth 20cm is half- fulled of water. 300 leadshots of same size are dropped into the jar and the level of water raises by 2.8 cm. find the diameter of each leadshots .

Answer 1

Answer:

The diameter of each leadshot = 1.4 cm

Step-by-step explanation:

Given:

Cylindrical Jar diameter = D = 14 cm

Depth of the jar = H = 20 cm

Initial Water level W1 = half od the jar = 10 cm

Water level raised by 2.8 cm

No of lea shots = 300

Let the diameter of the shots = d cm

1) Lets find out the volume of the water in the jar before dropping the shots.

Volume of the cylindircal shape given by

V = (π/4) × D² × h

Substituting  - D = 14 and height = water level = W1 = 10

V1 = (3.14/4) × 14² × 10

V1 = 1538.6 cm³ .....  Initial volume of water .... (1)

After dropping the 300 shots, water height increased by 2.8 cm.

New Water level W2 = 10 + 2.8 = 12.8 cm

Total volume occupied by the water and the shots

V2 =  (π/4) × D² × W2

Substituting  - D = 14 and height = water level = W2 = 12.8

V2 = (3.14/4) × 14² × 12.8

V2 = 1969.408 cm³   ....... (2)

Now, The new water level volume is combination of the volume of water and the volume of the lead shots.

If the volume of the single lead shot = Vs

we can write,

V2 = V1 + 300Vs

∴ 300Vs = V2 - V1

∴300Vs = 1969.408 - 1538.6

∴ 300Vs = 430.808 cm³

∴ Vs    =   1.436 cm³ ...... (3)   ... Volume of a single shot

To find diameter of the shot

Vs = (4/3) ×π × r³    .... Where r= Redius = d/2

∴1.436 = (4/3) × 3.14 × (d/2)³

∴ (d/2)³  =  (3 × 1.436) ÷ (4 × 3.14 )

∴ (d/2)³ = 0.343

∴ d/2 = ∛0.343

∴ d/2 = 0.7

∴ d = 1.4  cm

The diameter of each leadshot = 1.4 cm

Answer 2

Answer:

Diameter of a lead shot is 1.4 cm

Step-by-step explanation:

Given: Diameter of jar, d = 14 cm

           Depth/ height of the jar, h = 20 cm

Radius of jar, r =7 cm

Volume of water in jar = Half of volume of cylinder

                                     = $\frac{1}{2}\times\pi r^2h$

                                     = $\frac{1}{2}\times\frac{22}{7}\times7^2\times20$

                                     = $11\times7\times20$

                                     = 1540 cm³

After 300 lead shots water level rise to 2.8 cm

⇒ Height if jar become $\frac{20}{2}+2.8$ = 10 + 2.8 = 12.8 cm

Volume of water in jar after rise = volume of cylinder

                                     = $\pi r^2h$

                                     = $\frac{22}{7}\times7^2\times12.8$

                                     = $22\times7\times12.8$

                                     = 1971.2 cm³

⇒ Volume of water rise = volume of 300 lead shots

Volume of 300 lead shot = 1971.2 - 1540 = 431.2 cm³

Volume of 1 lead shot = $\frac{431.2}{300}$

                                     = 1.4373333 cm³

lead shot is of sphere shape

Volume of sphere = $\frac{4}{3}\pi r^3$

$\frac{4}{3}\pi r^3=1.4373333$

$\frac{4}{3}\times\frac{22}{7}\times r^3=1.4373333$

$\frac{88}{21}\times r^3=1.4373333$

$r^3=1.4373333\times\frac{21}{88}$

$r^3=0.3429999$

$r=\sqrt[3]{0.34299999}$

$r=0.7$

Diameter of a lead shot = 2 × 0.7 = 1.4 cm

Therefore, Diameter of a lead shot is 1.4 cm