Question

a cylinder with a top and bottom has a radius 2x+1 and height 2x-1 . Write a simplifed expression for its

a) surface area, SA= 2pie^2 + 2pierh

b) volume, where V=pier^2h

Answer 1

r = radius

h = height

A = Area

V = Volume


With the top and bottom, the surface area is:


A = 2 r ^ 2 pi + 2 r pi h

Volume is equal to the multiple of the area of the base and the height or V=(base area)(height).

V = r ^ 2 pi h


In this case:

r = 2 x + 1

h = 2 x - 1


A = 2 r ^ 2 pi + 2 r pi h =

2 pi r ( r + h ) =

2 pi ( 2 x + 1 ) ( 2x + 1 + 2 x - 1 ) =

2 pi ( 2 x + 1 ) 4 x =

8 pi ( 2 x + 1 ) x =

8 pi ( 2 x ^ 2 + x )


V = r ^ 2 pi h

V = ( 2 x + 1 ) ^ 2 pi ( 2 x - 1 ) =

pi ( 4 x ^ 2 + 4 x + 1 ) ( 2 x - 1 ) =

pi ( 4 x ^ 2 2 x + 4 x 2 x + 2 x - 4 x ^ 2 - 4 x - 1 ) =

pi ( 8 x ^ 3 + 4 x ^ 2 - 2 x - 1 )

Answer 2

Hi! Sorry I'm pretty sure that for r and h in the equation for SA there is multiplication instead of addition... also in the Volume equation when there are brackets, why did you add everything instead of adding in the brackets separately and then multiplying the result?