Question

A metallic solid cone is melted and cast into the form of a circular cylinder of the same base as that of the cone. If height of the cylinder is 5cm, What was the height of the cone?​

Answer 1

Answer:

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Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

As, a metallic solid Cone is melted and castes into the circular cylinder form.

So,

Volume of cone = Volume of cylinder

Height of circular cylinder (h1) = 5 cm

Let Height of cone be h.

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A. T. Q

$\sf{ \frac{1}{3}\pi{r}^{2}h_{2} = \pi{r}^{2}h} \\ \\ \sf{ \frac{1}{3} \cancel{\pi {r}^{2}}h= \cancel{ \pi {r}^{2}} \times 5 } \\ \\ \sf{ \frac{1}{3}h\: cm \: = 5 } \\ \\ \sf{1h = 5 \times 3} \\ \\ \sf{ h = 15 cm}$

$\large{\boxed{\purple{\sf{h = 15 \: cm}}}}$

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✪ Additional information :

$\boxed{\begin{minipage}{7 cm} Formula of cylinder \\ \\ Volume = \pi r^2 h \\ \\ Curved \: \: Surface \: \: Area = 2 \pi r h \\ \\ Total \: \: Surface \: \: Area =2 \pi r(r + h) \end{minipage}}$

$\rule{200}{2}$

$\boxed{\begin{minipage}{7 cm}Formula of cone\\ \\ Volume = \frac{1}{3} \pi r^2 h\\ \\ Total \: \: surface \: \: area = \pi r^2 + \pi r \sqrt{r^2 + h^2}\\ \\ Curved \: \: Surface \: \: area = \pi r\sqrt{r^2 + h^2} \end{minipage}}$

$\rule{200}{2}$

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