Question

A solid cylinder of radius 7 cm and
height 20 cm is made of material
whose density is 6 gm/cm Find its cost
at the rate of Rs. 100 per kilogram.​

Answer 1

${ \bold \orange { \underline{\large{Required \: Answer : - }}}} \:$

${ \bold \red { \underline{\large{Given : - }}}} \:$

A solid cylinder of radius 7 cm and height 20 cm.

Which is made up of material whose density is 6 g/cm.

${ \bold { \underline{\large{To \: Find : - }}}} \:$

Cost of material at the rate of Rs. 100 per kg .

$\large\boxed{\purple{\tt{ ⇝So\:let's \:do\:it\::-}}}$

$\large\tt\underline{\pink{Firstly\:let's \:find\:the\:volume\:of\:cylinder\::-}}$

$\large\sf\underline{\blue{Formula\:of \:volume\:of\:cylinder\::-}}$

$\large\underline{\boxed{\green{\sf{πr^2h}}}}$

$\large\sf\underline{\red{Let's \:put\:the\:values\:in\:the\:formula\::-}}$

:$\large\implies$ $π\:×\:r\:×\:r\:×\:h$

:$\large\implies$ $\dfrac{22}{7}\:×\:7\:×\:7\:×\:20$

:$\large\implies$ $\dfrac{22}{\cancel{7}}$$\:×\:$${\cancel{7}}$$\:×\:7\:×\:20$

:$\large\implies$ $22\:×\:7\:×\:20$

:$\implies$ $\underline{\boxed{3080\:cm^3}}$

$\large\underline{\boxed{\orange{\sf\therefore{Volume\:of\:given\:cylinder\::-\:3080\:cm^3}}}}$

$\large\sf\underline{\blue{We\:know\:the\:density\:of\:material\:=\:6g/cm}}$

$\large\sf\underline{\green{So\:let's \:find\:its\:mass}}$

$\large\underline{\boxed{\orange{\sf{Mass\:=\:Density\:×\:Volume}}}}$

$\large\tt\underline{\pink{So\:let's \:put\:all\:values\:in\:\:the\:formula\: :-}}$

:$\large\implies$ $Density\:×\:Volume$

:$\large\implies$ $6\:×\:3080$

:$\large\implies$ $18480g$

$\large\underline{\boxed{\orange{\sf\therefore{Mass\:of\:given\:cylinder\:=\:18480g}}}}$

According to the question :-

Now we had to find the cost of material at the rate of Rs. 100 per kilogram.

Now

Firstly let's convert 18480g into kg.

As there are 1000g in 1kg . So we will divide 18480g by 1000.

:$\large\implies$ $\dfrac{18480}{1000}$

:$\implies$ $\underline{\boxed{18.48kg}}$

$We\: know \:cost\: of \:material \:for\: 1kg \:-\: Rs.\:100.$

$\therefore \:Cost\: of \:material \:for \:18.48kg \:= \:18.48 \:× \:100$

: $\implies$ $\underline{\boxed {Rs.\: 1848}}$

$\large\underline{\boxed{\green{\sf\therefore{Cost\:of\:material\:used\:to\:made\:that\:cylinder\:=\:Rs.\:1848}}}}$

$\huge\underline{\underline{\sf{ \color{magenta}{♡solved♡} }}}$

______________________________________

$Some\: more \:formulas \:of \:cylinder\: :-$

$1.\:Volume\: of \:cylinder \:= \:πr^2h\:(We\:used\:this\:one)$

$2.\:Lateral \:surface \:area \:of \:cylinder\: = \:2πrh.$

$3.\: Total \:surface\: area \:of\: cylinder\: = \:2πr(h \:+ \:r).$

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${ \bold \red { \underline{\large{Important \: Note : - }}}} \:$

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Answer 2

Question :-

A solid cylinder of radius 7 cm and height 20 cm is made of material whose density is 6 gm/cm Find its cost at the rate of Rs. 100 per kilogram.

Given :-

• Radius of cylinder = 7cm

• Height of cylinder = 20cm

• Density = 6kg/cm

• Rate = Rs. 100 per kg

To find :-

• cost at the rate of Rs. 100 per kilogram.?

Formula used :-

$➠ \: volume \: \: \: \: = \pi {r}^{2}h$

$➠ \: mass \: \: \: \: \: = density \times volume$

Solution :-

$\:\sf\underline\red{Volume::-}\:$

$⟼ \: \: \: \: \: \pi {r}^{2}h$

$⟼ \: \: \: \: \: \dfrac{22}{7} \times 7 \times 7 \times 20$

$⟼ \: \: \: \: \: \dfrac{22}{\cancel{7}}\times {\cancel{7}} \times 7 \times 20$

$⟼ \: \: \: \: \: 22 \times 7 \times 20$

$⟼ \: \: \: \: \: 3080 {cm}^{3}$

Thus, volume = $3080{cm}^{3}$

_____________

• Density of material = 6kg/cm (given)

• Mass = ?

$⟹$ Mass = Density × volume

$⟹$ M = 6 × 3080

$⟹$ M = 18480g

As mass is in gram, firstly we will convert it into kilogram.

Well, we know = 1 kg = 1000 g

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\dfrac{18480}{1000}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 18.48kg

_____________

cost of material for 1 kg = Rs. 100

⠀ "⠀ "⠀ ⠀ " ⠀ ⠀ "⠀ 18.48kg = 18.48 × 100

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = Rs. 1848