Answer:
[tex] x = 2.5 [/tex]
Step-by-step explanation:
Surface area of cylinder = 2πr(h + r)
Volume of cylinder = πr²h
Given that S.A = Volume of the cylinder, therefore, we have:
2πr(h + r) = πr²h
Radius (r) is given as 2.5 cm
height (h) = x cm
Input the values and solve for x
2πr(h + r) = πr²h
2πr(h + r) = πr(rh)
2(h + r) = rh (πr cancels πr)
[tex] 2(x + 2.5) = 2.5*x [/tex]
[tex] 2x + 5 = 2.5x [/tex]
Subtract 2x from both sides
[tex] 2x + 5 - 2x = 2.5x - 2x [/tex]
[tex] 5 = 0.5x [/tex]
Divide both sides by 0.5
[tex] \frac{5}{0.5} = \frac{0.5x}{0.5} [/tex]
[tex] 2.5 = x [/tex]
[tex] x = 2.5 [/tex]
