Problema Solution

1. A toilet paper has the dimensions inner circle diameter 5cm, outer circle diameter 10cm and height 11cm. If the thickness of the paper is 1/5mm, find the length of paper on the roll?

Answer provided by our tutors

We can consider the toilet paper to be right hollow cylinder with dimensions with


r = 5/2 = 2.5 cm inner radius

R = 10/2 = 5 cm outer radius

h = 11 cm height


Then for the volume of the hollow cylinder we have V1 = pi*h*((R^2) - (r^2))


Also if we unroll the toilet paper we will get a cuboid with


l = length

w = 1/5 mm = 1/(5*10) cm width

h = 11 cm height


The volume of the cuboid is V2 = l*w*h


To find the length l we shell use the fact that the volume of the hollow cylinder equals the volume of the cuboid that is V1 = V2


pi*h*((R^2) - (r^2)) = l*w*h divide both sides by h*w


l = [pi*((R^2) - (r^2))] / w


l = [pi*(25 - 6.25)] / (1/(5*10)


l = pi*937.5 cm


l = 2943.75 cm approximately


The length of the toilet paper is 2943.75 cm approximately.