Question

Determine the Mass and Volume of rubber stoppers based on the following measurements:

Stopper #1:

Weight: 21.7486g

Top Surface diameter (S): 3.05cm

Bottom Surface diameter (s): 2.55cm

Slant Height (diagonal from bottom to top): 2.51cm

Stopper #2:

Weight: 7.5069g

Top surface diameter (S): 2.07cm

Bottom surface diameter (s): 1.03cm

Slant height (diagonal from bottom to top): 2.51cm

Appreciate it!

Answer 1

To determine mass divide the weight by 9.81 N. ( 1 kg weighs 9.81 newton)

To determine volume : The shape of stopper is that of a frustum (consider it as a cone whose pointed part is cut off)

Volume = πh(R²+r²+r*R)/3

Where r = radius in the smaller area and R is the radius in the larger area , h is the vertical height

Slant height is given it must be converted to vertical height by using pythagoras theorem

vertical height, h= ( L² - (R-r)²) ^0.5   where L is the slant height

Stopper 1:

Mass = 21.7486/9.81 = 2.217 g

Top radius,R = 3.05/2 = 1.5275cm

Bottom radius,r = 2.55/2 = 1.275cm

Vertical height, h = (2.51² - (1.5275- 1.275)² )^0.5 = 2.4972cm

volume= 3.14*2.4972(1.5275²+ 1.275² + 1.5275 *1.275 )/3 = 15.445 cm³

Stopper 2:

Mass = 7.5069/9.81 = 0.7652 g

Top radius,R = 2.07/2 = 1.035cm

Bottom radius,r = 1.03/2 = 0.515cm

Vertical height, h = (2.51² - (1.035- 0.515)² )^0.5 = 2.455cm

volume= 3.14*2.455(1.035²+ 0.515² + 1.035 *0.515 )/3 = 4.8cm³