Question

How much ice cream can be put into a cone with base radius 7 cm and height 15 cm ?​

Answer 1

$\sf Given \begin{cases} & \sf{Radius\:of\:cone,\: r = \bf{7\;cm}} \\ & \sf{Height\;of\;cone,\:h = \bf{15\;cm}} \end{cases}$

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

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$\setlength{\unitlength}{1.8mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{7 cm}}\put(14,10){\sf{15 cm}}\end{picture}$

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

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

$:\implies\sf Volume_{\;(cone)} = \dfrac{1}{ \cancel{3}} \times \dfrac{22}{7} \times (7)^2 \times \cancel{15}$

$:\implies\sf Volume_{\;(cone)} = \dfrac{22}{ \cancel{7}} \times \cancel{49} \times 5$

$:\implies\sf Volume_{\;(cone)} = 22 \times 7 \times 5$

$:\implies{\underline{\boxed{\frak{\purple{Volume_{\;(cone)} = 770\;cm^3 }}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Amount\;of\;ice-cream\:that\;can\;be\;put\;into\:a\;cone\;is\; \bf{770\;cm^3}.}}}$

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

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area \:formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Hollow\:cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

Answer 2

Step-by-step explanation:

Given, radius,r=3.5 cm

r=

10

35

cm

r=

2

7

cm

Height,h=12 cm

Volume of cone=

3

1

π.r

2

.h

=

3

1

.

7

22

.(

2

7

)

2

.12

=154 cm

3