Question

A manufacturer involves twelve children in colouring pen stands all over excluding base which are in the shape of a cylinder made of wood of thickness 2 cm. The inner radius of the cylinder is 4 cm and its height is 14 cm. Find the area they had to paint if 50 pen stands were given to them for painting.

Answer 1

area that the manufacturer hav to paint in 50 stands = 50 x 2πRh x π(R^2- r^2)
= 50 x 2 x 22/7 x 6 x 14 x 22/7 ( 36-16)
= 100 x 44 x 6 x 22/7 x 20
u can solve it by using calculator

Answer 2

Find the area painted as follows: 

Find the outer surface area of the cylindrical pencil stand.
 Area of the outer cylinder surface is:

Perimeter of the cylinder × height of the cylinder

πD  × H =  22/7 × 12 × 14 
              = 528 cm²

Area of the inner cylindrical part: (assuming that the base is 2cm thick as well)
The inner height would be 12 cm


πD  × H = 22/7 × 8 × 12
              =  301.632cm²


The area of the top part painted: 
Area of the larger circular surface - smaller surface

πR² - πr² = 3.142×6² - 3.142 × 4²
                = 113.112 - 50.272
                = 62.84cm²

Add the area to find the total area painted:

 528 cm²   +  62.84cm²  +   301.632cm² = 892.472cm²

The area painted in 1 stand is 892.472 cm²

The area of 50 such stands is    892.472 cm² × 50 = 44623.60 cm²