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."

Answer 1

this is due tmrw and im on the verge of a breakdown 💀

Answer 2

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

Answer 3

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/(4π) * 24πy^3 = 18
r = ∛18

Answer 4

go with Bosnian. My typo didn't include the y.

Answer 5

tysm!! i got 100% :))