Question

A right cylinder has a base area of 81π cm2. Its height is 2 times the radius. Identify the lateral area and the surface area of the cylinder, rounded to the nearest tenth.

I keep getting 324 as my lateral area and 810 as my surface area. :\ It's not the right answer, apparently. :3 Can someone please explain?

Answer 1

S(s)=S(b)+S(l)
S(b)=81π

S(b)=πR²
πR²=81π
R²=81
R=√81
R=9
h=2R
h=2*9=18
S(l)=2πRh=2π*9*18=324π≈100,5 - the lateral area
S(s)=2*81π+324π=162π+324π=486π≈1526,8 - the surface area

Answer 2

base area=area of circle =pi(r^2)=81pi
pi(r^2)=81pi
divide both sides by pi
r^2=81
square root
r=9
heigth is 2 times radius
9 times 2=18

lateral area= area around the cylinder minus the circles on top and bottom =circumference times height=2pi(r)(h)=2pi(9)(18)=324pi cm^2

surface area=lateral area+circles on top and bottom=2p(r)(h)+2(pi(r^2))=324pi+2(pi(9^2))=324pi+2(pi(81))=324pi+162pi=486pi cm^2
aprox them

pi = aprox 3.14
324 times 3.14=1017.36 cm^2
486 times 3.14=1525.04 cm^2
you did something wrong in the surface area calculatrion