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

Answer 1

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

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 :

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

______________________________________________________