if a hollow sphere of internal and external diameter 4cm melted 8cm respectively melted into a cone of base diameter 8cm . find the height of cone
amount of solid in the original sphere
= (4/3)π(4^3) - (4/3)π(2^3)
= (4/3)π(64-8)
= 224π/3
This must become the volume of a cone
(1/3)π(4^2)h = 224π/3
time 3/π
16h = 224
h = 14 cm
To find the height of the cone formed when a hollow sphere melts into it, we can use the concept of volumes.
First, let's calculate the volume of the hollow sphere. The formula for the volume of a hollow sphere is:
V = (4/3) * π * (R^3 - r^3)
Where:
V is the volume of the hollow sphere,
π is a mathematical constant approximately equal to 3.14159,
R is the external radius of the hollow sphere (half of the external diameter), and
r is the internal radius of the hollow sphere (half of the internal diameter).
In this case, the external diameter is 4 cm, so the external radius is 2 cm. Similarly, the internal diameter is also 4 cm, so the internal radius is 2 cm.
Plugging these values into the formula, we get:
V = (4/3) * π * (2^3 - 2^3)
V = (4/3) * π * (8 - 8)
V = 0
Therefore, the volume of the hollow sphere is zero because the internal and external radii are equal. This means that the hollow sphere has no volume.
Since the hollow sphere completely melted into the cone, the volume of the hollow sphere should be equal to the volume of the cone. We can calculate the volume of the cone using the formula:
V = (1/3) * π * r^2 * h
Where:
V is the volume of the cone,
r is the radius of the base of the cone (half of the base diameter), and
h is the height of the cone.
In this case, the base diameter is 8 cm, so the radius is 4 cm.
Since the volume of the cone is also zero, we can set up the following equation:
0 = (1/3) * π * (4^2) * h
Simplifying the equation, we get:
0 = (1/3) * π * 16 * h
0 = (16/3) * π * h
To solve for h, we can divide both sides of the equation by (16/3) * π :
0 / ((16/3) * π) = h
Therefore, the height of the cone is 0 cm.
In conclusion, when a hollow sphere of internal and external diameter 4 cm melts into a cone of base diameter 8 cm, the height of the cone is 0 cm.