Respuesta :
Answer:
To find the diameter of the base of
the cone formed when the solid
cylinder is melted, we can use the
concept of volume conservation.
The volume of the solid cylinder is
equal to the volume of the solid
cone. 1. **Volume of the Cylinder:**
The formula for the volume of a
cylinder is given by: Veylinder = Tr2h
where:-r=8cm (radius of the
cylinder) -h = 2 cm (height of the
cylinder) Substitute the values:
Veylinder =T x 82 x 22. **Volume of
the Cone:** The formula for the
volume of a cone is given by:
Vcone = 3T12h where:-h= 6 cm
(height of the cone) - r is the radius
of the base of the cone - Since the
radius of the cylinder and cone are
the same, let's denote the radius of
the base of the cone as r as well.
Substitute the values and set the
volumes equal:
" x 82 x 2 = 3tr2 x 6 3. *Solve cylinder) Substitute the values:
Veylinder =T x 82 x 22. **Volume of
the Cone:** The formula for the
volume of a cone is given by:
Vcone = 3T h where:-h = 6 cm
(height of the cone)- r is the radius
of the base of the cone - Since the
radius of the cylinder and cone are
the same, let's denote the radius of
the base of the cone as r as well.
Substitute the values and set the
volumes equal:
T x 82 x 2 = 3tr2 x 6 3. *Solve for
r:** 128g = 2tr264 =r2 r = 8 cm 4.
**Diameter of the Base of the
Cone:** The diameter of the base of
the cone is twice the radius:
Diameter=2r=2x8=16 cm
Therefore, the diameter of the base
of the cone formed is 16 cm.
