219k views
1 vote
SAT question, level of difficulty: HARD

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

User Eliane
by
7.7k points

2 Answers

4 votes


S=2\pi (5^(2) )+2\pi (5)h\\h=(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=(S-50\pi )/(10\pi ) \\h=(S)/(10\pi) - (50\pi )/(10\pi ) \\h=(S)/(x)-y = (S)/(10\pi) - 5\\y = 5

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

User Deramko
by
8.0k points
4 votes

Answer:

y = 5

Step-by-step 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 =
(S)/(x) -y

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 = (2π * 50) + (10π h)

S = 50π + 10π h

S - 50π = 10π 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 =
(S)/(x) -y

and x and y are constants.

x = 10π as constant

y = 5 as constant

hope it clears your mind.

User KooiInc
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.