What happens to the Surface area and volume of a cylinder if the radius and height are divided by 2?

Answer 1

If the radius and height are divided by two, the surface area will decrease by the square of 2, i.e. by a factor of 4, and the volume will decrease by the cube of 2, i.e. by a factor of 8.

For SA ≡ Surface Area, V ≡ volume, r ≡ radius, and h ≡ height,

SA = 2πr2 + 2πrh

And

V = 2πr2h

For r1 and h1 as the original radius and height respectively and r2 and h2 being the new radius and height respectively, r1=2r2 and h1 = 2h2, and the ratio between the old and new SA and V would be:

SA2/SA1 = [2πr22 + 2πr2h2]/[2πr12 + 2πr1h1]

= [2πr22 + 2πr2h2]/[2π(2r2)2 + 2π(2r12h1)]

= [2πr22 + 2πr2h2]/4[2πr22 + 2πr2h2]

= ¼

V2/V1 = [2πr22h2]/[2πr12h1]

= [2πr22h2]/[2π(2r2)2(2h2)]

= [2πr22h2]/8[2πr22h2]

= 1/8