Question

A cone has a base radius of 5cm and a height of 12cm.calculate (a) its slant height ( b) curved surface area Please tell the answer only

Answer 1

★ Given :

$\begin{lgathered}\bullet\:\:\textsf{Radius = \textbf{5 cm}}\\\bullet\:\:\textsf{Height = \textbf{12 cm}}\end{lgathered}$

$\rule{130}1$

★ Solution :

$\dashrightarrow\sf\:\: l = \sqrt{h^2 + r^2}\\\\\\\dashrightarrow\sf\:\: l = \sqrt{12^2 + 5^2}\\\\\\\dashrightarrow\sf\:\: l = \sqrt{144 + 25}\\\\\\\dashrightarrow\sf\:\: l = \sqrt{169}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf l = 13\:cm}}\:\:\:\:\Bigg\lgroup \bf{Slant\: height}\Bigg\rgroup$

$\therefore\:\underline{\textsf{Slant height of the cone is \textbf{13}} \: \sf{cm}}.$

$\rule{130}1$

$:\implies\sf CSA \:of\: cone = \pi r l \\\\\\:\implies\sf CSA \:of\: cone = \pi \times 5 \times 13\\\\\\:\implies\sf CSA \:of\: cone = 3.14 \times 65 \\\\\\:\implies\underline{\boxed{\sf CSA \:of\: cone = 204.1\:cm^2}}$

$\therefore\:\underline{\textsf{Median Height of the distribution is \textbf{204.1}} \: \sf{cm^2}}.$

$\rule{170}2$

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

Answer 2

AnswEr :

• Slant height of the cone is 13 cm.

• Curved Surface Area (CSA) is 204.1 cm².

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GiveN :

• Base radius of the cone = 5 cm

• Height of the cone = 12 cm

To FinD :

• Slant height of the cone = ?

• Curved Surface Area(CSA) = ?

SoluTion :

By using the formulae,

☯ Slant height of the Cone :

$:\implies \sf \: \: \: l = \sqrt{ {h}^{2} + {r}^{2} } \\ \\ \\ \\ :\implies \sf \: \: \:l = \sqrt{ {12}^{2} + {5}^{2} } \\ \\ \\ \\ :\implies \sf \: \: \:l = \sqrt{144 + 25} \\ \\ \\ \\ :\implies \sf \: \: \:l = \sqrt{169} \\ \\ \\ \\ :\implies \sf \: \: \:{\underline{\boxed{\sf{\purple{l = 13 \: cm}}}}}\: \bigstar$

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☯ Curved Surface Area of the Cone :

$:\implies \sf \: \: \: CSA = \pi rl \\ \\ \\ \\ :\implies \sf \: \: \:CSA = 3.14 \times 5 \times 13 \\ \\ \\ \\ :\implies \sf \: \: \:CSA = 3.14 \times 65 \\ \\ \\ \\ :\implies \sf \: \: \:{ \underline{ \boxed{ \sf{ \blue{CSA = 204.1 \: {cm}^{2}}}}}} \: \bigstar$

$\therefore$ Slant height and curved surface area of the cone are 13 cm and 204.1 cm²,respectively!!

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★ Extra formulae related to cone :

1. Volume = 1/3πr²h

2. Total Surface Area (TSA) = πr² + πrl

3. Base Area = πr²

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