Question

$\large {\dag \; {\underline{\underline{\red{\pmb{\textbf{\textsf{ \; Question \; :- }}}}}}}}$

$\longmapsto$ The height and the slant height of a cone are 21 cm and 28 cm respectively . Find :-



◕ Radius of the Cone
◕ Volume of the Cone


$\\ {\underline{\rule{200pt}{5pt}}}$

$\green{\textsf{ Thanks in Advance :D }}$​

Answer 1

Step-by-step explanation:

$\pmb{\color{darkcyan} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}}$

$\\ \rule{500pt}{0.1pt}$

$\text{We have, \( \sf h=21 cm \) and \( \sf l=28 cm \).}$

$\\ \[ \begin{aligned} \tt \therefore \quad l^{2}=r^{2}+h^{2} \Rightarrow r & \tt=\sqrt{l^{2}-h^{2}}=\sqrt{(28)^{2}-(21)^{2}} cm \\ \\ \tt \Rightarrow r & \tt=\sqrt{(28+21) \times(28-21)} cm =\sqrt{49 \times 7} cm \\ \\ & \tt=7 \sqrt{7} cm . \end{aligned} \]$

$\\ \text{Volume of the cone \( \tt=\dfrac{1}{3} \pi r^{2} h \)}$

$\\ \[ \begin{array}{l} \tt =\left\{\dfrac{1}{3} \times \dfrac{22}{7} \times(7 \sqrt{7})^{2} \times 21\right\} cm ^{3} \\ \\ \tt =(22 \times 343) cm ^{3} \\ \\ \red{ \tt=7546 cm ^{3} } \end{array} \]$