SOLUTION: A cylindrical rod of length "h" is melted and cast into a cone of base radius twice that one of the cylinder. What is the height of the cone??.. please reply... THANKYOU VERY MUCH
Algebra.Com
Question 923589: A cylindrical rod of length "h" is melted and cast into a cone of base radius twice that one of the cylinder. What is the height of the cone??.. please reply... THANKYOU VERY MUCH
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Vc = = Vcone =
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the volume of the cylinder is equal to the volume of the cone.
the length of the cylinder is equal to the height of the cylinder.
the volume of the cylinder is equal to pi * r^2 * h
the volume of the cone is equal to 1/3 * pi * (2r)^2 * x
x is the height of the cone.
since their volumes are equal, you get:
pi * r^2 * h = 1/3 * pi * (2r)^2 * x
simplify to get:
pi * r^2 * h = 1/3 * pi * 4r^2 * x
simplify further to get:
pi * r^2 * h = 4/3 * pi * r^2 * x
divide both sides of this equation by pi * r^2 and you get:
h = 4/3 * x
solve for x and you get:
x = 3/4 * h
the height of the cone will be 3/4 * the height of the cylinder and the radius of the base of the cone will be 2 times the radius of the base of the cylinder and the volume of the cone will be equal to the volume of the cylinder.
to test, give some values to r and h and see if the volumes are the same.
let r = 3 and h = 8 for the cylinder.
then 2r = 6 and 3/4 * h = 6 and you get:
r = 6 and h = 6 for the cone.
the volume of the cylinder will be pi * r^2 * h = pi * 3^2 * 8 = 72 * pi.
the volume of the cone will be 1/3 * pi * r^2 * h = 1/3 * pi * 6^2 * 6 = = 72 * pi.
the volumes are the same so the formula looks good.
RELATED QUESTIONS
A cylindrical rod of length "h" is melted and cast into a cone of base radius twice that... (answered by rothauserc)
The radius of cross-section of a solid cylindrical rod of iron is 50cm the cylinder is... (answered by mananth)
A sphere of radius x is melted and its volume
is divided into two equal parts. One part... (answered by greenestamps)
A solid cylinder of gold, height 14cm and base radius 8cm, is melted down and cast as a... (answered by josgarithmetic)
A solid metal cylinder of height 1.2 metres and diameter 0.8 metres is melted down and... (answered by josgarithmetic)
A cylinder is drawn in a cone of height, H, and base, R. If the height and radius of the... (answered by josgarithmetic)
The height of one metallic cylindrical rod is 6 centimeters and its radius is 3... (answered by Fombitz)
The height of one metallic cylindrical rod is 6 centimeters and its radius is 3... (answered by Fombitz)
a metal sphere with a radius of 3 cm is melted down and formed into a cylinder with a... (answered by josgarithmetic)