Question
"The diagram shows a solid cylinder. The cylinder has a radius of 2y and height of 6y.
The cylinder is melted down and made into a sphere of radius r.
Express r in terms of y."
The cylinder is melted down and made into a sphere of radius r.
Express r in terms of y."
Answers
<3
this is due tmrw and im on the verge of a breakdown 💀
Bosnian
volume of cylinder:
Area of circle • height =
( 2 y)^2π • 6 y = 4 y^2 π • 6 y =
24 y^3 π
When the cylinder is melted down volume of material is same.
volume of sphere:
4 / 3 r^3 π
24 y^3 π = 4 / 3 r^3 π
Divide both dides by 4 π
6 y^3 = r^3 / 3
Multiply both sided by 3
18 y^3 = r^3
r^3 = 18 y^3
r = ∛18 y
Area of circle • height =
( 2 y)^2π • 6 y = 4 y^2 π • 6 y =
24 y^3 π
When the cylinder is melted down volume of material is same.
volume of sphere:
4 / 3 r^3 π
24 y^3 π = 4 / 3 r^3 π
Divide both dides by 4 π
6 y^3 = r^3 / 3
Multiply both sided by 3
18 y^3 = r^3
r^3 = 18 y^3
r = ∛18 y
oobleck
for a cylinder,
v = πr^2 h = π(2y)^2 * 6y = 24πy^3
for a sphere,
v = 4/3 πr^3 = 24πy^3
so r^3 = 3/(4Ï€) * 24Ï€y^3 = 18
r = ∛18
v = πr^2 h = π(2y)^2 * 6y = 24πy^3
for a sphere,
v = 4/3 πr^3 = 24πy^3
so r^3 = 3/(4Ï€) * 24Ï€y^3 = 18
r = ∛18
oobleck
go with Bosnian. My typo didn't include the y.
<3
tysm!! i got 100% :))