Question

1. Find the volume of the right circular cone with (1) radius 6 cm, height 7 cm (ii) radius 3.5 cm, height 12 cm​

Answer 1

Answer:

Question :

Find the volume of the right circular cone with,

» (1) radius 6 cm, height 7 cm

» (ii) radius 3.5 cm, height 12 cm

$\rule{300}{1.5}$

Solution :

As we know that,

$\small{\pink{\underline{\boxed{\bf{Volume \: of \: cone = \dfrac{1}{3} \pi{r}^{2} h}}}}}$

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(1) radius 6 cm, height 7 cm

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \pi{r}^{2} h}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times (6)^{2} \times 7}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times (6 \times 6)\times 7}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times 36\times 7}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{\cancel{7}}\times 36\times \cancel{7}}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times 22\times 36}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{\cancel{3}} \times 22\times \cancel{36}}}}$

${\longrightarrow{\rm{VOLUME = 1 \times 22 \times 12}}}$

${\longrightarrow{\rm{VOLUME = 22 \times 12}}}$

${\longrightarrow{\rm{\red{VOLUME = 264 \: {cm}^{3}}}}}$

Hence, the volume of cone is 264 cm³.

$\rule{190}1$

(ii) radius 3.5 cm, height 12 cm

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \pi{r}^{2} h}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times (3.5)^{2} \times 12}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times (3.5 \times 3.5)\times 12}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{3} \times \dfrac{22}{7} \times 12.25\times 12}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{1}{\cancel{3}} \times \dfrac{22}{7} \times 12.25\times \cancel{12}}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{22}{7} \times 12.25\times 4}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{22}{7} \times 49}}}$

${\longrightarrow{\rm{VOLUME = \dfrac{22}{\cancel{7}} \times \cancel{49}}}}$

${\longrightarrow{\rm{VOLUME = 22 \times 7}}}$

${\longrightarrow{\rm{\red{VOLUME = 154 \: {cm}^{3}}}}}$

Hence, the volume of cone 154 cm³.

$\rule{300}{1.5}$

Learn More :

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$

$\rule{220pt}{4pt}$