Question

$\huge\mathcal\red{Question:}$
The pie chart shows the preference of 240 children for various sports. Calculate the actual number of children who like each sport. ━━━━━━━━━━━━━━━━━
The pic of Pie chart is shown Above [⬆] ━━━━━━━━━━━━━━━━━
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Answer 1

Answer:

$\displaystyle{{\boxed{\red{\sf\:No.\:of\:children\:like\:football\:=\:60}}}}$

$\displaystyle{{\boxed{\pink{\sf\:No.\:of\:children\:like\:hockey\:=\:20}}}}$

$\displaystyle{{\boxed{\green{\sf\:No.\:of\:children\:like\:cricket\:=\:80}}}}$

$\displaystyle{{\boxed{\blue{\sf\:No.\:of\:children\:like\:tennis\:=\:50}}}}$

$\displaystyle{{\boxed{\red{\sf\:No.\:of\:children\:like\:badminton\:=\:30}}}}$

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given a pie chart showing the distribution of preference for various sports of 240 children.

We have to find the actual number of children who like each sport.

Now,

Total number of children = 240

Let,

$\displaystyle{\bullet\:\sf\:Central\:angle\:=\:\theta}$

$\displaystyle{\bullet\:\sf\:Total\:number\:of\:children\:=\:N\:=\:240}$

Now, we know that,

The measure of a circle is 360°.

$\displaystyle{\therefore\:\boxed{\pink{\sf\:No.\:of\:children\:like\:x\:sport\:=\:\dfrac{\theta\:for\:the\:x\:sport}{360}\:\times\:N}}}$

Now,

For football,

$\displaystyle{\sf\:\theta\:=\:90^{\circ}}$

$\displaystyle{\sf\:No.\:of\:children\:like\:football\:=\:\dfrac{\theta}{360}\:\times\:N}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:football\:=\:\dfrac{9\cancel{0}}{36\cancel{0}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:football\:=\:\cancel{\dfrac{9}{36}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:football\:=\:\dfrac{1}{4}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:football\:=\:\cancel{\dfrac{240}{4}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:No.\:of\:children\:like\:football\:=\:60}}}}$

─────────────────────────

Now,

For hockey,

$\displaystyle{\sf\:\theta\:=\:30^{\circ}}$

$\displaystyle{\sf\:No.\:of\:children\:like\:hockey\:=\:\dfrac{\theta}{360}\:\times\:N}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:hockey\:=\:\dfrac{3\cancel{0}}{36\cancel{0}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:hockey\:=\:\cancel{\dfrac{3}{36}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:hockey\:=\:\dfrac{1}{12}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:hockey\:=\:\cancel{\dfrac{240}{12}}}$

$\displaystyle{\implies\underline{\boxed{\pink{\sf\:No.\:of\:children\:like\:hockey\:=\:20}}}}$

─────────────────────────

Now,

For cricket,

$\displaystyle{\sf\:\theta\:=\:120^{\circ}}$

$\displaystyle{\sf\:No.\:of\:children\:like\:cricket\:=\:\dfrac{\theta}{360}\:\times\:N}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:cricket\:=\:\dfrac{12\cancel{0}}{36\cancel{0}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:cricket\:=\:\cancel{\dfrac{12}{36}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:cricket\:=\:\dfrac{1}{3}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:cricket\:=\:\cancel{\dfrac{240}{3}}}$

$\displaystyle{\implies\underline{\boxed{\green{\sf\:No.\:of\:children\:like\:cricket\:=\:80}}}}$

─────────────────────────

Now,

For tennis,

$\displaystyle{\sf\:\theta\:=\:75^{\circ}}$

$\displaystyle{\sf\:No.\:of\:children\:like\:tennis\:=\:\dfrac{\theta}{360}\:\times\:N}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:tennis\:=\:\cancel{\dfrac{75}{360}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:tennis\:=\:\dfrac{5}{\cancel{24}}\:\times\:\cancel{240}}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:tennis\:=\:5\:\times\:10}$

$\displaystyle{\implies\underline{\boxed{\blue{\sf\:No.\:of\:children\:like\:tennis\:=\:50}}}}$

─────────────────────────

Now,

For badminton,

$\displaystyle{\sf\:\theta\:=\:45^{\circ}}$

$\displaystyle{\sf\:No.\:of\:children\:like\:badminton\:=\:\dfrac{\theta}{360}\:\times\:N}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:badminton\:=\:\cancel{\dfrac{45}{360}}\:\times\:240}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:badminton\:=\:\dfrac{3}{\cancel{24}}\:\times\:\cancel{240}}$

$\displaystyle{\implies\sf\:No.\:of\:children\:like\:badminton\:=\:3\:\times\:10}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:No.\:of\:children\:like\:badminton\:=\:30}}}}$

Answer 2

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

$\pink{\overbrace{ \underbrace{ \red{\mid\star\mid \:\: \purple{ } } \:\: \red{\mid\star\mid}}}}$

EXPLANATION IN DETAILS

$\large\underline\bold{GIVEN,}$

$\leadsto Central\:angle\:=\:\theta \\ \leadsto\:Total\:number\:of\:children\:=\:N\:=\:240 \\ \therefore Now,\: we\: know\: that,</p><p>\:The\: measure \:of \:a \:circle\: is\: 360^{\circ}.$

$\large\underline\bold{TO\:FIND,}$

$\green{ \circ\: actual\:no.\:who\:like\:each\:sport.}$

$\bf{ \mathcal{ \underline{\orange{Using\:}}}} \\ \\ \rm{ \boxed{ \underline{ \red{ No.\:of\:children\:like\:x\:sport\:=\:\dfrac{\theta\:for\:the\:x\:sport}{360}\:\times\:N}}}}$

$\large\underline\bold{SOLUTION,}$

$\therefore \: For \:football, \\ \\ :\implies \theta\:=\:90^{\circ} \\ \\ :\implies \:\dfrac{\theta}{360}\:\times\:N \\ \\ :\implies \\\ \\ :\implies \dfrac{9\cancel{0}}{36\cancel{0}}\:\times\:240 \\ \\ :\implies \:\cancel{\dfrac{9}{36}}\:\times\:240\\ \\ :\implies \:\dfrac{1}{4}\:\times\:240\\ \\ :\implies \:\cancel{\dfrac{240}{4}}\\ \\ \red{ \underline{ \overline{ \mid\:\: No.\:of\:children\:like\:football\:=\:60\:\:\mid}}}$

$\\ \\ \therefore\: For\: hockey, \\ \\ :\implies \theta\:=\:30^{\circ} \\ \\ :\implies \:\dfrac{\theta}{360}\:\times\:N\\ \\ :\implies \dfrac{3\cancel{0}}{36\cancel{0}}\:\times\:240 \\ \\ :\implies \:\cancel{\dfrac{3}{36}}\:\times\:240 \\ \\ :\implies \dfrac{1}{12}\:\times\:240\\ \\ :\implies \:\cancel{\dfrac{240}{12}} \\ \\ \red{ \underline{ \overline{ \mid\:\:No.\:of\:children\:like\:hockey\:=\:20\:\:\mid}}}$

$\\ \\ \therefore \:For\: cricket,\\ \\ :\implies \theta\:=\:120^{\circ} \\ \\ :\implies \:\dfrac{\theta}{360}\:\times\:N\\ \\ :\implies\\ \\ :\implies \dfrac{12\cancel{0}}{36\cancel{0}}\:\times\:240 \\ \\ :\implies \:\cancel{\dfrac{12}{36}}\:\times\:240\\ \\ :\implies \dfrac{1}{3}\:\times\:240 \\ \\ :\implies \:\cancel{\dfrac{240}{3}} \\ \\ \red{ \underline{ \overline{ \mid\:\:\:No.\:of\:children\:like\:cricket\:=\:80\:\:\mid}}}$

$\\ \\ \therefore\: For\: tennis, \\ \\ :\implies \:\theta\:=\:75^{\circ} \\ \\ :\implies \:\dfrac{\theta}{360}\:\times\:N \\ \\ :\implies \cancel{\dfrac{75}{360}}\:\times\:240 \\ \\ :\implies \dfrac{5}{\cancel{24}}\:\times\:\cancel{240} \\ \\ :\implies \:5\:\times\:10</p><p> \\ \\ \red{ \underline{ \overline{ \mid\:\:No.\:of\:children\:like\:tennis\:=\:50\:\:\mid}}}$

$\\ \\ \therefore \:For\: badminton,\\ \\ :\implies \theta\:=\:45^{\circ} \\ \\ :\implies \:\dfrac{\theta}{360}\:\times\:N \\ \\ :\implies \:\cancel{\dfrac{45}{360}}\:\times\:240 \\ \\ :\implies \:\dfrac{3}{\cancel{24}}\:\times\:\cancel{240} \\ \\ :\implies \:3\:\times\:10 \\ \\ \red{ \underline{ \overline{ \mid\:\:No.\:of\:children\:like\:badminton\:=\:30\:\:\mid}}}$

$\\ \large{\mathfrak{\red{\underline{\overline{ never\:play\:with\:legends.}}}}}$