Question

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20) The lateral surface area of a hollow cylinder is 4224 cm". It is cut along its height
and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular
dieer​

Answer 1

Given :

Lateral Surface Area of a cylinder : 4224 cm²

When it's cut along its height we get a rectangular sheet of width 33 cm.

Solution :

We can easily understand taht the curved surface of the cylinder is equal to the area of the rectangle formed by cutting from the question

$\purple{ \implies{ \sf \: C.S.A \: of \: cylinder = Area \: of \: rectangle}}$

$\sf \implies4224 = length \times breadth \\ \sf \implies 4224 = length \times 33 \\ \sf \implies 4224 \div 33= length$

$\sf \implies128cm$

Hence , we have got the length of the sheet and now it will be easier to calculate the perimeter of the sheet as we already know the dimensions of the rectangular sheet !

$\sf \purple{\implies {Perimeter \: of \: a \: rectangle \: = 2(l + b)}}$

$\sf \implies2(128 + 33) \\ \sf \implies2 \times 161 \\ \sf \implies322cm$

Therefore , the perimeter of the rectangle is 322cm

Answer 2

$\huge \bold \red {hola \: mate}$

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).

$\orange{ \boxed{ \boxed{cylinder - }}}$

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

$\rule{300}{1.5}$

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 the perimeter of the rectangular

sheet = 322cm