Math, asked by nikitadnaz, 3 months ago

Calculate the amount of ice cream that can be put into a cone with base radius 3.5 cm and height 12 cm. ​

Answers

Answered by SarcasticL0ve
24

\sf Given \begin{cases} & \sf{Radius\:of\:cone,\: r = \bf{3.5\;cm}}  \\ & \sf{Height\;of\;cone,\:h = \bf{12\;cm}}  \end{cases}\\ \\

To find: Amount of ice cream that can be put into a cone?

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\setlength{\unitlength}{1.8mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{3.5 cm}}\put(14,10){\sf{12 cm}}\end{picture}

\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\

  • Amount of ice - cream that can be put in a cone = Volume of cone

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\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\

\star\;{\boxed{\sf{\pink{Volume_{\;(cone)} = \dfrac{1}{3} \pi r^2 h}}}}\\ \\

:\implies\sf Volume_{\;(cone)} = \dfrac{1}{ \cancel{3}} \times \dfrac{22}{7} \times (3.5)^2 \times \cancel{12}\\ \\

:\implies\sf Volume_{\;(cone)} = \dfrac{22}{ \cancel{7}} \times \cancel{12.25} \times 4\\ \\

:\implies\sf Volume_{\;(cone)} = 22 \times 1.75 \times 4\\ \\

:\implies\sf Volume_{\;(cone)} = 88 \times 1.75\\ \\

:\implies{\underline{\boxed{\frak{\purple{Volume_{\;(cone)} = 154\;cm^3 }}}}}\;\bigstar\\ \\

\therefore\:{\underline{\sf{Amount\;of\;ice-cream\:that\;can\;be\;put\;into\:a\;cone\;is\; \bf{154\;cm^3}.}}}

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\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}\\ \\

\boxed{\begin{minipage}{6.5 cm}\bigstar$\:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \:Area = Area\:of\:Base + CSA\\{\quad\:\:\:\:\:\qquad\qquad\qquad\quad=\pi r^2+\pi rl}\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume \: of \: cone=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant  \: height\: of \: cone=\sqrt{h^2 + r^2}\end{minipage}}


Cosmique: Incredible! ❤ •,•
Answered by Anonymous
19

Answer:

Given :-

  • Radius of cone = 3.5 cm
  • Height of cone = 12 cm

To Find :-

Amount of ice cream that can be put into a cone

Solution :-

So, for finding the amount of ice cream we will find Volume.

 \huge \bf \: Volume =  \frac{1}{3} \pi \:  {r}^{2} h

 \sf \: Volume \:  =  \dfrac{1}{3}  \times  \dfrac{22}{7}  \times  {3.5}^{2}  \times 12

 \sf \: Volume \:  = 1 \times  \dfrac{22}{7}  \times 12.25 \times 4

 \sf \: Volume = 22 \times 1.75 \times 4

 \sf \: Volume = 88 \times 1.75

 \sf \: Volume = 154 \:  {cm}^{3}

Amount of ice−cream that can be put into a cone is 154cm³.

Diagram :-

 \setlength{\unitlength}{1.8mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{3.5 cm}}\put(14,10){\sf{12 cm}}\end{picture}


Cosmique: Fantastic!!
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