A hemispherical bowl of internal diameter 36 cm contains liquid .this liquid is filled into cylindrical bottles or diameter 6 cm . find the height of each bottle if 10 % liquid is wasted in on this transfer.?

Question

Answer

Radius of each cylindrical bottle, R = 6/2 = 3 cm

Let the height cylindrical bottle be h

volume of each cylindrical bottle = πR2h

= π x 3 x3 x h

Therefore, Total volume of 72 such cylindrical bottles

= π x 3 x3 x h x 72

= 648 πh^2 cm^3

According to the question,

Total volume of 72 such cylindrical bottles = volume of the liquid transferred

Therefore, 648 πh = 3499.2π

⇒ h = 3499.2/648

⇒ h = 5.4 cm

Hence, the height of each cylindrical bottle is 5.4 cm

Answer

How did you know that total bottle is 72....@@zaharaa Ansari as it is not given in question....

Answer

Solution:

Given:
Internal diameter of the hemispherical bowl = 36 cm
Diameter of the cylindrical bottle = 6 cm

To find:
The height of each bottle after transferring the liquid with 10% wastage.

Formula Used:
Volume of a hemisphere = (2/3) * π * r^3
Volume of a cylinder = π * r^2 * h

Let's solve this step by step:

1. Calculate the volume of the hemispherical bowl:
Given that the internal diameter of the bowl is 36 cm, the radius (r) of the bowl can be calculated as half of the diameter, which is 18 cm.
Using the formula for the volume of a hemisphere, we can calculate the volume of the bowl as:
Volume of the bowl = (2/3) * π * (18)^3

2. Calculate the total volume of liquid in the bowl:
Since the bowl is completely filled with liquid, the total volume of the liquid is equal to the volume of the bowl.

3. Calculate the volume of each cylindrical bottle:
Given that the diameter of the cylindrical bottle is 6 cm, the radius (r) of the bottle can be calculated as half of the diameter, which is 3 cm.
Using the formula for the volume of a cylinder, we can calculate the volume of each bottle as:
Volume of each bottle = π * (3)^2 * h

4. Calculate the wastage:
Given that 10% of the liquid is wasted during the transfer, the remaining liquid is 90% of the total volume.
So, the volume of liquid after wastage = 90% of the total volume of liquid.

5. Calculate the number of bottles required:
Divide the volume of liquid after wastage by the volume of each bottle to find the number of bottles required.

6. Calculate the height of each bottle:
Using the formula for the volume of a cylinder, rearrange it to solve for the height (h) of each bottle:
h = (Volume of each bottle) / (π * (3)^2)

7. Substitute the values and calculate the height of each bottle.

Therefore, the height of each bottle, considering a 10% wastage, can be calculated using the given formulas and steps explained above.

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