Question

The diameter of a garden roller is 1.4 m and it is 2 m long. Find the maximum area covered by it in 50 revolutions

Answer 1

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Answer 2

$\huge{\underline{\sf{Question :-}}}}$

The diameter of a garden roller is 1.4 m and it is 2 m long. Find the maximum area covered by it in 50 revolutions.

$\huge{\underline{\sf{Answer :-}}}}$

$\sf Given\begin{cases} &\sf{Diameter\;of\;the\; garden\:roller,\:D\;=\be{1.4\:m}}\\&\sf{Width\;of\;the\;garden\: roller,\:h=\;\bf{2\:m}}\end{cases}$

$\boxed{ \sf \red{ To \: Find : }}$

✏ Area it will cover in 5 revolutions = ❓

$\green{\underline\bold{We \:know\:,}}$

✏ Radius, r = $\frac{Diameter}{2}$

✏ r = $\frac{1.4}{2}$

✏ r = 0.7 m

$\green{\underline\bold{From\:the\:formula,}}$

$\boxed{ \sf \blue{Area \: of\:the\:roller=\: Curved\:surface\:area\:of\:the\:cylinder }}$

= 2Πrh

= 2 × $\frac{22}{7}$ × 0.7 × 2

= 8.8 m sq.

$\green{\underline\bold{Now,}}$

$\boxed{ \sf \blue{ Area\: of \:the\: roller\: it\:will\:cover\: in\: 1 \:revolution=\:area\:of\:the\:roller }}$

= 8.8 m sq.

$\boxed{ \sf \blue{ Area\: of \:the\: roller\: it\:will\:cover\: in\:50 \:revolutions= }}$

= 8.8 × 50

= 440 m sq.

$\pink{\underline\bold{∴The\:required\:answer\:is\: = \: 440\: m\: sq.}}$

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