Question

How much ice-cream can be put into a cone with base radius 3.5 cm and slant height 12.5cm​

Answer 1

$\sf Given \begin{cases} & \sf{Radius\;of\;cone,\;r = \bf{3.5\;cm}} \\ & \sf{Slant\;height\;of\;cone,\;l = \bf{12.5\;cm}} \end{cases}$

To find: How much ice-cream can be put into a cone?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀

$\setlength{\unitlength}{1.8mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(15,1.6){\sf{3.5 cm}}\put(14.5,10){\sf{h}}\put(21,10){\sf{12.5 cm}}\end{picture}$

⠀⠀

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

$\star\;{\boxed{\sf{\pink{(slant\;height)^2 = (Base)^2 + (Height)^2}}}}$

$:\implies\sf l^2 = b^2 + h^2$

$:\implies\sf (12.5)^2 = (3.5)^2 + h^2$

$:\implies\sf h^2 = (12.5)^2 - (3.5)^2$

$:\implies\sf h^2 = 156.25 - 12.25$

$:\implies\sf h^2 = 144$

$:\implies\sf \sqrt{h^2} = \sqrt{144}$

$:\implies{\underline{\boxed{\frak{\purple{h = 12\;cm}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Height\; of\;cone\;is\; \bf{12\;cm}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

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

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

⠀⠀

Therefore,

⠀⠀

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

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

$:\implies\sf Volume_{\;(cone)} = \dfrac{1}{ \cancel{3}} \times \dfrac{22}{7} \times 12.5 \times \cancel{12}$

$:\implies\sf Volume_{\;(cone)} = \dfrac{22}{7} \times 12.5 \times 4$

$:\implies{\underline{\boxed{\frak{\purple{Volume_{\;(cone)} = 157.1428\;cm^3}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Amount\; of\;ice-cream\;that\;can\;be\;put\;into\;a\;cone\;is\; \bf{157.1428\;cm^3}.}}}$

Answer 2

Answer:

radius,r = 3.5cm

slant height,l = 12.5cm

Step-by-step explanation:

l^2 = b^2 + h^2

(12.5)^2= (3.5)^2 + h^2

156.25 = 12.25+ h^2

156.25 - 12.25 = h^2

144 = h^2

12cm = h

Quantity of ice-cream = Volume of cone

= 1 / 3 πr^2h

= 1/3 × 22/7 (3.5×3.5) (12)

= 22/7 (3.5×3.5) (4)

= 22/7 (12.25) (4)

= 22/7 (49)

= 1078/7

= 154cm^3