A veesel is in the form of an inverted cone. Its hieght 8cm and radius of top which is open is 5cm. It is filled with water up to brim. When lead shots each of which is a sphere of radius 0.5cm are dropped into the vessels, one -forth of water flows out.find the number of lead shots dropped into the vessel?

Question

Answer

No.of sphere ×volume of sphere =volume of vessel (cone)no. of sphere = volume of vessel                           / volume of sphere

Answer

A vessels full of water is in the form of an inverted cone of height 8cm and the radius of its top,which is open is 5cm.100 spherical lead balls are dropped into the vessel.one-fourth of the water flows out of the vessel.find the radius of a spherical bal.Ye Question lagraha wo nhi banparaha hai

Answer

Problem:
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top, which is open, is 5 cm. The vessel is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped into the vessel.

Solution:

Step 1: Find the volume of the vessel:

The vessel is in the shape of an inverted cone. The formula to find the volume of a cone is given by:

V = (1/3) * π * r^2 * h,

where V is the volume, π is a constant approximately equal to 3.14159, r is the radius, and h is the height.

Given that the radius of the top of the vessel is 5 cm and the height is 8 cm, we can substitute these values into the formula:

V = (1/3) * 3.14159 * 5^2 * 8,
V = 104.719755 cm^3.

Therefore, the volume of the vessel is 104.719755 cm^3.

Step 2: Find the volume of one lead shot:

The formula to find the volume of a sphere is given by:

V = (4/3) * π * r^3,

where V is the volume and r is the radius.

Given that the radius of each lead shot is 0.5 cm, we can substitute this value into the formula:

V = (4/3) * 3.14159 * 0.5^3,
V = 0.523599 cm^3.

Therefore, the volume of one lead shot is 0.523599 cm^3.

Step 3: Find the number of lead shots:

One-fourth of the water flows out when the lead shots are dropped into the vessel. This means that the volume of water remaining in the vessel after the shots are dropped is three-fourths of the original volume.

Let's assume the number of lead shots dropped into the vessel is N.

The volume of N lead shots is N * 0.523599 cm^3.

The remaining volume of water in the vessel is 3/4 * 104.719755 cm^3.

Therefore, we can set up the equation:

N * 0.523599 = 3/4 * 104.719755.

Simplifying the equation:

N = (3/4 * 104.719755) / 0.523599,
N = 62.831853 / 0.523599,
N ≈ 120.

Therefore, approximately 120 lead shots were dropped into the vessel.

Conclusion:
The number of lead shots dropped into the vessel is approximately 120.

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