Question

the curved surface of a cylinder is 264 m².its volume is 924 m³.the height of the cylinder must be: 

Answer 1

lateral surface area = 2π r h = 264 m^2 

volume = π r^2 h = 924 m^3 

solve for r: 
r/2 = 3.5 

so r = 7 m 

now you can find height in terms of π ! 

archimedes

Answer 2

Al = 264[m²] ⇔ 2rπh = 264[m²] 
V = 924[m³] ⇔ r²πh = 924[m³] 

⇒ V / Al = (r²πh) / (2rπh) = r / 2 = (924[m³]) / (264[m²]) = 3.5[m] 
⇒ r = 2 × 3.5[m] = 7[m] 

⇒ Al = 2 × 7[m] × π × h 
⇒ h = (264[m²]) / (π × 14[m]) 
⇒ h ≈ 6[m]