Question

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

Answer 1

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

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

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

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

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

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

Answer 2

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 :-

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