from a closed cardboard cylinder of height 30 cm and diameter of base 21 CM 15 rectangle of size 2 cm × 51.5 cm are cut out .find the total surface area of the remaining cylinder.
Answers
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The remaining surface area of the cylinder is 1128 cm².
• Given data :
Height of the cardboard cylinder is 30 centimetres.
Diameter of the base of the cardboard cylinder is 21 centimetres.
Length of the rectangle 51.5 centimetres and breadth of the rectangle 2 centimetres.
Total number of rectangular pieces is 15.
• The radius of the base of the cardboard cylinder is :
= Diameter/2
= 21/2
= 10.5 centimetres
• Now we have to calculate the curved surface area of the cardboard cylinder by using the following mathematical formula :
= 2×π×radius×height
= 2 × 22/7 × 10.5 × 30
= 1980 cm²
• Now,we have to calculate the base area of the cardboard cylinder by using the following mathematical formula :
= π × (10.5)²
= 22/7 × (10.5)²
= 346.5 cm²
• Now,we have to calculate the total surface area of the cardboard cylinder by using the following mathematical formula :
= Curved surface area + (2×Base area)
= 1980+ (2×346.5)
= 1980+693
= 2673 cm²
• Now, we have to calculate the area of one rectangular piece by using the following mathematical formula
= Length × Breadth
= 51.5×2
= 103 cm²
• Now, we have to calculate the total area of the rectangular pieces by using the following mathematical formula :
= Total number of the rectangular pieces × area of one rectangular piece
= 15 × 103
= 1545 cm²
So,the remaining area of the cardboard is
= (2673-1545)
= 1128 cm² (Answer)