# algebra, mathematics

"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."

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1. this is due tmrw and im on the verge of a breakdown ðŸ’€

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2. volume of cylinder:

Area of circle â€¢ height =

( 2 y)^2Ï€ â€¢ 6 y = 4 y^2 Ï€ â€¢ 6 y =

24 y^3 Ï€

When the cylinder is melted down volume of material is same.

volume of sphere:

4 / 3 r^3 Ï€

24 y^3 Ï€ = 4 / 3 r^3 Ï€

Divide both dides by 4 Ï€

6 y^3 = r^3 / 3

Multiply both sided by 3

18 y^3 = r^3

r^3 = 18 y^3

r = âˆ›18 y

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3. for a cylinder,
v = Ï€r^2 h = Ï€(2y)^2 * 6y = 24Ï€y^3
for a sphere,
v = 4/3 Ï€r^3 = 24Ï€y^3
so r^3 = 3/(4Ï€) * 24Ï€y^3 = 18
r = âˆ›18

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

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5. tysm!! i got 100% :))

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