Question

the diameter of a roller is 84cm and its length is 120cm. it takes 500 complete revolutions to move once over to level a playground. find the area of the playground in m².​

Answer 1

Step-by-step explanation:

${\Large{\bf{\underline{\pink{Question :}}}}}$

The diameter of a roller is 84cm and its length is 120cm. it takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m².

${\Large{\bf{\underline{\pink{Solution :}}}}}$

Given :

• Length of roller = 120 cm
• Diameter of roller = 84 cm

To find out :

• Area of playground in m²

${\large{\red{✏ \: \: \: \: }}}{\bold{\rm{For \: better \: understanding \: refer \: to \: the \: attachment}}}$

Further calculations :

${\bold{\boxed{\sf{\orange{Radius \: of \: roller \: = \: \frac{Diameter}{2}}}}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: \frac{84}{2} \: = \: 42 cm}}}$

${\large{\red{✠ \: \: \: \: \: }}}{\bold{\rm{\underline{According \: to \: the \: question :}}}}$

Area of roller = curved surface area of cylinder

Therefore

${\bold{\sf{⟼ \: \: \: \: \: \: Curved \: Surface \: Area \: of \: cylinder \: = \: 2πrh }}}$

${\bold{\sf{⟼ \: \: \: \: \: Curved \: Surface \: Area \: of \: cylinder \: = \: \Big(2 \: × \: \frac{22}{7} \: × \: 42 \: × \: 120\Big) cm²}}}$

${\bold{\sf{⟼ \: \: \: \: \: Curved \: Surface \: Area \: of \: cylinder \: = \: 31608cm²}}}$

${\Large{\red{✰ \: \: \: \: }}}{\bold{\rm{Area \: of \: 1 \: revolution \: = \: Area \: of \: roller \: = \: 31608 cm²}}}$

${\Large{\red{✰ \: \: \: \: \: }}}{\bold{\rm{Area \: of \: 500 \: revolution \: = \: 500 \: × \: 31608 cm²}}}$

${\Large{\red{✰ \: \: \: \: \: }}}{\bold{\rm{Area \: of \: 500 \: revolution \: = \: 15840000cm²}}}$

Also,

${\Large{\red{✰ \: \: \: \: \: }}}{\bold{\rm{Area \: of \: playground \: = \: 15840000cm²}}}$

Let's convert the area in m²

${\bold{\sf{: \: ⟹ \: \: \: \: \: 15840000 cm² \: = \: 15840000 \: × \: \frac{1}{100 } \: × \: \frac{1}{100}m²}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: 1584 \: m²}}}$

Hence the area of playground is 1584 m²

Answer 2

$\small \bold{Radius \: of \: the \: roller (r)= \frac{84}{2} = 42 \: cm}$

length of the roller (h)=120cm

∴ Area of the playground levelled in taking 1 complete revolution 2πrh

$\small \bold{= 2×227×42×120=31680 \: {cm}^{2} }$

∴ Area of the playground

$\small \bold{=31680×500=15840000 \: {cm}^{2} }$

$\bold{= \frac{15840000}{100 \times 100} {m}^{2} = 1584 {m}^{2} }$