Question

A cylindrical roller is 28 cm in diameter and 1 m wide.
(a) Find, in cm2
, the curved surface area of the roller.
(b) Calculate in m2
, the area covered by the roller in 25 revolutions.

Answer 1

$\large\underline{\sf{Solution-}}$

Given :-

• Diameter of cylindrical roller, d = 28 cm

• Height of cylindrical roller, h = 1m = 100 cm

To Find :-

• Curved Surface Area of roller in square cm.

• Area covered by roller in 25 revolutions.

Formula Used :-

$\red{ \boxed{ \sf{ \:CSA_{(Cylinder)} = 2\pi \: r \: h }}}$

where,

• r is radius of cylinder

• h is height of cylinder.

$\red{ \boxed{ \sf{1 \: m \: = \: 100 \: cm}}}$

Calculations :-

Given that,

↝ Diameter of cylindrical roller, d = 28 cm

So,

↝ Radius of cylindrical roller, r = 14 cm

↝ Height of cylindrical roller, h = 1m = 100 cm

We know,

↝ Curved Surface Area of cylindrical roller, is

$\rm :\longmapsto\:CSA_{(Cylinder)} = 2 \: \pi \: r \: h$

$\rm \: \: = \: 2 \times \dfrac{22}{7} \times 14 \times 100$

$\rm \: \: = \: 8800 \: {cm}^{2}$

$\bf\implies \:CSA_{(Cylindrical \: roller)} = 8800 \: {cm}^{2}$

Now,

We know that

↝ Area covered in 1 revolution = Curved Surface Area of cylindrical roller.

So,

$\rm :\longmapsto\:Area \: covered \: in \: 1 \: revolution = 8800 \: {cm}^{2}$

Hence,

$\rm :\longmapsto\:Area \: covered \: in \:25 \: revolution = 8800 \times 25$

$\rm \: \: = \: 8800 \times 25 \times \dfrac{1}{1000} \: {m}^{2}$

$\rm \: \: = \: 220 \: {m}^{2}$

$\bf :\longmapsto\:Area \: covered \: in \:25 \: revolution = 220 \: {m}^{2}$

Additional Information :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²