Mathematics: Acylindrical-shaped cup has a height of 7 centimeters and a volume of 112 cubic centimeters. henry fills the cup completely full of water. he then pours the water from the cup and completely fills a cone. if the cone has the same radius as the cup, what is the height of the cone?

Since both angles lie upon a straight line their sum must be 180°.180-a=b and we are given that a=11°b=180-11b=169°...

Acylindrical-shaped cup has a height of 7 centimeters

Ответ:

MalikaJones

10.03.2022

let's bear in mind that the cylinder and the cone both have the same volume of 112 cm³, and the same radius, but different heights.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=112\\ h=7 \end{cases}\implies 112=\pi r^2(7)\implies \cfrac{112}{7\pi }=r^2\implies \cfrac{16}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{16}{\pi }}=r\implies \cfrac{\sqrt{16}}{\sqrt{\pi }}=r\implies \cfrac{4}{\sqrt{\pi }}=r \\\\[-0.35em] ~\dotfill$

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \qquad \begin{cases} r=\frac{4}{\sqrt{\pi }}\\ V=112 \end{cases}\implies 112=\cfrac{\pi \left( \frac{4}{\sqrt{\pi }} \right)^2(h)}{3} \\\\\\ 336=\pi \left( \cfrac{4^2}{(\sqrt{\pi })^2} \right)h\implies 336=\pi \cdot \cfrac{16h}{\pi }\implies 336=16h \\\\\\ \cfrac{336}{16}=h\implies \blacktriangleright 21=h \blacktriangleleft$

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Acylindrical-shaped cup has a height of 7 centimeters and a volume of 112 cubic centimeters. henry fills the cup completely full of water. he then pours the water from the cup and completely fills a cone. if the cone has the same radius as the cup, what is the height of the cone?

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