sarshaly
contestada

SAT question, level of difficulty: HARD
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The surface area, S, of a cylinder with a radius of 5 is defined by [tex]S = 2\pi(5^{2}) + 2\pi(5)h[/tex], where h is the height of the cylinder. If the equation is rewritten in the form [tex]h = \frac{S}{x}-y[/tex], where x and y are constants, what is the value of y ? (Surface Area [tex]= 2\pi rh+2\pi r^{2}[/tex])
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The answer is y = 5, but I can't figure out how, please help.

Respuesta :

ricchad

Answer:

y = 5

Explanation:

S = 2π r² + 2π r h

let r = 5

let h = height of the cylinder

since the equation is re-written in the form h = [tex]\frac{S}{x} -y[/tex]

where x and y are constants.

what is the value of y?

S = (2π r²) + (2π r h)  ------ plug in r = 5

S = (2π * 5²) + (2π * 5 * h)

S = (2Ï€ * 50) + (10Ï€ h)

S = 50Ï€ + 10Ï€ h

S - 50Ï€ = 10Ï€ h

     S - 50π

h = -------------

         10π

       S         50π

h = ------  -  ---------

     10π         10π

       S        

h = ------  -  5

     10π      

therefore,  the value of y = 5

remember the re-written equation  h = [tex]\frac{S}{x} -y[/tex]

and x and y are constants.

x = 10Ï€ as constant

y = 5 as constant

hope it clears your mind.

tossmysalad

[tex]S=2\pi (5^{2} )+2\pi (5)h\\h=\frac{S}{x} -y\\\\\S=2\pi (5^{2} )+2\pi (5)h\\S=2\pi (25)+10\pi h\\S= 50\pi +10\pi h\\10\pi h= S-50\pi \\h=\frac{S-50\pi }{10\pi } \\h=\frac{S}{10\pi} - \frac{50\pi }{10\pi } \\h=\frac{S}{x}-y = \frac{S}{10\pi} - 5\\y = 5[/tex]

This is a simplified version of ricchad's answer, all credit goes to that person.