Math, asked by qirgyfygw, 8 months ago

The diameter of the base of a right circular cone is 6 cm and height is 4 cm. Then the slant height of the cone is a) 7 cm b) 6 cm c) 5 cm d) 4 cm

Answers

Answered by Anonymous
2

\bf\huge\blue{\underline{\underline{ Question : }}}

The diameter of the base of a right circular cone is 6 cm and height is 4 cm. Then the slant height of the cone is

a) 7 cm

b) 6 cm

c) 5 cm

d) 4 cm

\bf\huge\blue{\underline{\underline{ Solution : }}}

Given that,

  • \tt\:\leadsto Diameter_{(Cone)} = 6\:cm.
  • \tt\:\leadsto Height_{(Cone)} = 4\:cm.

To find,

  • \tt\:\leadsto Slant\:Height_{(Cone)} = ?\:cm.

Formula :

\boxed{\tt{\red{ Slant\: Height : l = \sqrt{ h^{2} + r^{2} }}}}

  • Radius (r) = ?

\tt\:\implies Radius = \frac{d}{2} = \frac{6}{2} = 3

  • Substitute the values.

\bf\:\implies l = \sqrt{(4)^{2} + (3)^{2}}

\bf\:\implies l = \sqrt{16 + 9}

\bf\:\implies l = \sqrt{25}

\bf\:\implies l = 5

\underline{\boxed{\bf{\purple{\therefore Slant\:Height_{(Cone)} = 5\:cm.}}}}\:\orange{\bigstar}

More information :

$$\begin{lgathered}\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}}} \:\:CSA = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA\\{\quad\:\:\:\qquad=\pi r^2+\pi rl}\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\end{minipage}}\end{lgathered}

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