An ice cream cone is 12 cm deep and 6 cm in diameter. A single scoop of vanilla ...

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marianneizabellec @marianneizabellec

October 2022 1 2 Report

An ice cream cone is 12 cm deep and 6 cm in diameter. A single scoop of vanilla ice cream 6 cm in diameter is placed on top. If the ice cream melts into the cone, will it overflow? Why? Note: 1 scoop = half of a sphere

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$\large \bold {SOLUTION}$

$\small\textsf{Use the formula of a cone} \\ \\ \sf\blue{V_{cone} = \pi{r} ^{2} \frac{h}{3} }$

$\small\sf{Let \: \pi = 3.14 \: and \: r = 3 \: cm}$

$\small\sf{V = \pi{r} ^{2} \dfrac{h}{3}}$

$\small\sf{V = \pi({3} )^{2} (\dfrac{6}{3})}$

$\small\sf{V = \pi(9 ) (2)}$

$\small\sf{V =18 \pi}$

$\small\boxed{\green{\sf{V≈ 56.55 \: {cm}^{3} }}}$

$\small\textsf{Use the sphere formula for the area of the scoop}$

$\small\textsf{Take note that the scoop is half of a sphere}$

$\sf\blue{V_{scoop} = \dfrac{ \frac{4}{3}\pi {r}^{3} }{2} }$

$\small\sf{Let \: \pi = 3.14 \: and \: r = 3 \: cm}$

$\small\sf{V_{scoop} = \dfrac{ \frac{4}{3}\pi {r}^{3} }{2}}$

$\small\sf{V_{scoop} = \dfrac{ \frac{4}{3}\pi ({3})^{3} }{2}}$

$\small\sf{V_{scoop} = \dfrac{ \frac{4}{3}(27\pi) }{2}}$

$\small\sf{V_{scoop} = \dfrac{ \frac{108\pi}{3} }{2}}$

$\small\sf{V_{scoop} = \dfrac{ 36\pi}{2}}$

$\small\sf{V_{scoop} = 18\pi}$

$\small\boxed{\green{\sf{V_{scoop}\approx56.55 \: {cm}^{3} }}}$

We can say that the volume of the cone and the scoop of ice-crem has an equal value. Hence the scoop will not overflow. When the ice-cream melts, it will be only excatly full.

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