The lateral surface of a hollow cylinder is 2400 square centimetre. It is cut along its height and formed into a rectangular sheet of width 12 cm. Find the perimeter of the rectangular sheet.
Answers
Answer
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Surface area:
The surface area of a solid is the sum of the areas of the plane or curved faces of the solid.
It is measured in square units such as square centimetre (cm²) and square metre (m²).
Cylinder:
Whenever we talk about a total surface area of a cylinder the cylinder must be closed at both the ends by two circular regions or it should be a cylindrical solid object.
Total surface area of a solid cylinder= curved surface area + sum of the areas of two circular ends of the cylinder
= 2πrh+ 2πr²
Total surface area of a solid cylinder= 2πr(h+r)
The lateral surface area of the curved surface area of a cylinder= 2πrh
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Solution:
Length of rectangle will be equal to the circumference (2πr) of a circular end and the breadth will be equal to the height h of the cylinder.
Given:
Lateral surface area of hollow cylinder= 4224 cm²
Height of a hollow cylinder (h)= 33 cm
Lateral surface area or curved surface area of hollow cylinder= 2πrh
4224 = 2×(22/7) × r × 33
r=(4224×7) / 2×22×33
r= (64 × 7)/22
Length of rectangular sheet= 2πr
= 2×(22/7)× (64 × 7)/22
=64 × 2
= 128 cm
Perimeter of rectangular sheet = 2(l+b)
= 2(128+33)
= 2 × 161
= 322 cm
Hence, perimeter of rectangular sheet is 322 cm.
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