Question

he lateral surface area of a hollow cylinder is 7392cm2 . If it is cut along its height and a rectangular sheet of width 42cm is formed, then the perimeter of the rectangular sheet is

Answer 1

HELLO DEAR,

we know:-

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

AND

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 =

7392cm²

Height of a hollow cylinder (h) = 42 cm

Lateral surface area or curved surface area

of hollow cylinder= 2πrh

so, 7392 = 2× (22/7) × r × 42

7392 = 2 × 22 × r × 6

r = $\bold{\frac{7392}{2*22*6}}$

r = $\bold{\frac{168}{6}}$

r = 28cm

Length of rectangular sheet= 2πr

= 2 × (22/7) × 28

= 2 × 22 × 4

= 176 cm

Perimeter of rectangular sheet = 2(l + b)

= 2(176 + 42)

= 2 × 218

= 436 cm

Hence, perimeter of rectangular sheet is

436 cm.

I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Since the cylinder is cut along its height, the circumference of its base (or top) 

= width of rectangular sheet i.e. 2πR=44cm

Curved Surface Area of a Cylinder =2πRh

Given 2πRh=5632h=2πR5632=445632cm=128cm

The length of the sheet will be the height.

Required perimeter =2(l+b)=2(128+44)cm=344cm