Question

the lateral surface area of a hollow cylinder us 422cm square it is cut along its height and formed a rectangular sheet of with 33cm find the perimeter of rectangular sheet​

Answer 1

$\huge \fbox \purple{❥ Answer}$

$\huge \fbox \green{ Mensuration:}$

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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$\huge \fbox \orange{ Solution:}$

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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Hope this will help you....

Answer 2

Step-by-step explanation:

l=422÷33=12.7

perimeter=2(12.7+33)=91.4cm

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