The volume of a cylinder with a height-to-radius ratio of 4:1 is [tex]108 \pi[/tex] cubic centimeters. Find the radius and height of the cylinder.

H : r = 4 : 1 r H ​ = 1 4 ​ → H = 4 r ( ∗ ) V = 108 π c m 3 V = π r 2 H s u b s t i t u t e ( ∗ ) π r 2 ⋅ 4 r = 108 π / : 4 π r 3 = 27 r = 3 27 ​ r = 3 ( c m ) H = 4 r = 4 ⋅ 3 = 12 ( c m ) A n s w er : r a d i u s = 3 c m an d h e i g h t = 12 c m .

Answered by Anonymous | 2024-06-10

4:1 height to radius let x be radius let 4x be height
V=(pi)(r)^2h 108(pi)=(pi)x^2(4x) divide both sides by pi 108=x^2(4x) 108=4x^3 divide both sides by 4 27=x^3 cube root both sides x=3
therefore the radius is 3 and the height is 12

Answered by deathstrike001 | 2024-06-10

The radius of the cylinder is 3 cm, and the height is 12 cm based on the given height-to-radius ratio and volume. The calculation involved using the volume formula and solving for the unknowns step-by-step.
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Answered by Anonymous | 2024-12-24