Question

2. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base
is 24.m.
​

Answer 1

Given
Slant height, l = 21 m
Radius, r = 12 m

Solution
TSA of cone = pi * r * (r + l)
= (22/7) * 12 * (12+21)
= (22/7) * 12 * 33
= (22/7) * 396
= 8712/7
= 1244.57 cm^2

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 2.\:\: Find \:the\: total\: surface\: area\: of\: a\: cone\:, if\: its\: slant\\\tt height\: is\: 21 \:m\: and\: diameter \:of\: its\: base\: is\: 24\:m.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf Slant\: height\: of\: the\: cone =21\:m$
• $\sf \bf Diameter\: of\: the\: cone =24\:m$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf Total \:Surface \:Area \:of \:the \:cone(TSA)$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Radius \:of \:the \:cone}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {r=\dfrac{d}{2}}}}}}}}$

• $\sf r=radius \:of \:the \:cone$
• $\sf d=diameter\:of \:the \:cone$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies r=\dfrac{24}{2}$

$\implies {\blue {\boxed {\boxed{\purple {{\sf r=12}}}}}}$

————————————————————————————

${\pink {\underline {\bf {\pmb {Total\:Surface \:Area\:of \:the \:cone}}}}}$

${\blue {\boxed {\boxed {\boxed {\green{\pmb {TSA={\pi} r\big(r+l\big)}}}}}}}$

• $\sf TSA=Total \:surface \:area \:of \:the \:cone$
• $\sf r=radius \:of \:the \:cone$
• $\sf l=slant \:height \:of \:the \:cone$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies TSA=\dfrac{22}{7}\times 12\Big(12+21\Big)$

$\bf \implies TSA=\dfrac{22}{7}\times 12\times 33$

$\bf \implies TSA=\dfrac{22}{7}\times 396$

$\bf \implies TSA=\dfrac{8712}{7}$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {TSA=1244.57\:{cm}^{2}}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\red {\sf {\pmb{{\therefore} The\:Total \:Surface \:Area \:of \:the\:cone \:is\:1244.57\:{cm}^{2}}}}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Curved \:surface \:area \:of \:cone = \pi r l$

$\sf Total\:surface \:area \:of \:cone = \pi r(r+l)$

$\sf Volume\:of \:cone = \dfrac{1}{3}\pi{r}^{2}h$