Two right cylinders are similar. The surface areas are 24 and 96m. What is the ratio of the volumes of the Cylinders

Answer 1

SA = 24 and 96

SA = 2pir^2 + 2pirh

1st cylinder surface area = 24 = 2hpir+2pir^2

12 = hpir + pir^2= pir(h+r)

2nd cylinder surface area = 96 = 2piHR+2piR^2

48= piR(H+R)

96/24= 4 = (HR^+R^2)/(hr+r^2)

V1= hpir^2

V2= HpiR^2

V2/V1= HR^2/hr^2

let R=1/pi, 48=pi(1/pi)(H+1/pi) H=(48pi-1)/pi)= about 47.682

let r= 1/pi, 12= (h+1)/pi h = (12pi-1)/pi= about 11.682

V2/V1= (49pi-1)/(13pi-1)= about 47.682/11.682= about 4.082

volume ratio = about 4 if radii are equal r=R=1/pi

let heights be =H=h =(1+pi)/pi

then r=12, R=48

V2/V1 = R/r = 48/12= 4

volume ratio = 4 = surface area ratio