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.
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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
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
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external radius=6cm,(R=6cm)internal radius=4cm(r=4cm).so t.s.a=2π14×10+2π10=942.47cm².so area of 50pen stands=47123.5cm²
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