find base area of larger cylinder if smaller one has area of 64 cm.

Question

volumes of 2 similar shapes are in the ratio 686:128

Answer 1

Volume of a cylinder = pi x r² x height 

or volume = area of the base x height

 

Using the ratio of the volumes, let the volume of the smaller cylinder =128.

 

the height of the larger cylinder is some constant k times the height of the smaller cylinder = kh

 

the radius of the larger cylinder is some constant k times the radius of the smaller cylinder = kr

 

volume of the larger = pi (kr)² x kh

 

volume of the larger =pi·k²r²·kh

 

   = k³pi·r²h

 

from the information given, let pi·r²h = 128

 

686 = k³·128

 

686/128 = k³

 

k = 1.75

 

base area of larger cyliner = pi·(kr)²

 

= pi·(1.75)²r²

 

we know that pi·r² =64

 

base area of larger = (1.75)²(64)

 

= 196