Question

CSA of a cone is 154 cm square and its slant height is 14 cm. Find its radius and TSA of cone​

Answer 1

Given :

• Curved Surface Area of Cone is 154 cm .
• Slant Height of Cone is 14 cm .

To Find :

• Radius and Total Surface Area of Cone .

Solution :

For Radius :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{154=\dfrac{22}{{\cancel{7}}}\times{r}\times{{\cancel{14}}}}$

$\longmapsto\tt{154=22\times{r}\times{2}}$

$\longmapsto\tt{154=44\:r}$

$\longmapsto\tt{\cancel\dfrac{154}{44}=r}$

$\longmapsto\tt\bf{3.5=r}$

So , The Radius of Cone is 3.5 cm .

Now ,

For Total Surface Area :

Using Formula :

$\longmapsto\tt\boxed{T.S.A\:of\:Cone=\pi{r(l+r)}}$

Putting Values :

$\longmapsto\tt{\dfrac{22}{{\cancel{7}}}\times\dfrac{{\cancel{35}}}{10}\times{(14+3.5)}}$

$\longmapsto\tt{\dfrac{11{\not{0}}}{1{\not{0}}}\times{17.5}}$

$\longmapsto\tt{11\times{17.5}}$

$\longmapsto\tt\bf{192.5\:{cm}^{2}}$

So , The Total Surface Area of Cone is 192.5 cm² .

Answer 2

$\underline{ \sf \:Given:-}$

• $\small \sf Curved \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \boxed{ \bf \purple{ 154 \: cm}}$
• $\small \sf \: Slant \: Height \: of the \: Cone, (l) \large \leadsto \small \boxed{ \bf \purple{ 14 \: cm}}$

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$\underline{ \sf \: To \: Find:- }$

• $\small \sf \: radius \: (r) \large \leadsto \small \: ?$
• $\small \sf \: Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small { \bf { ? }}$

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$\underline{ \sf \: SoluTion:- }$

$\small \sf \:: \longrightarrow Curved \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf \pi rl$

$\small \sf \:: \longrightarrow 154 \large \leadsto \small \bf \frac{22} {\cancel{7} } \times r \times \cancel{14}$

$\small \sf \:: \longrightarrow 154 \large \leadsto \small \bf 44 \: r$

$\small \sf \:: \longrightarrow \frac{154}{44} \large \leadsto \small \bf r$

$\small \sf \:: \longrightarrow r \large \leadsto \small \bf \frac {\cancel{{154}}}{ \cancel{44}}$

$\small \sf \:: \longrightarrow r \large \leadsto \small \bf \frac{7}{2}$

$\small \sf \therefore \: Hence \: we \: got \: the \: radius (r) \: as \: \frac{7}{2}$

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$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf \pi r(l + r)$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf \frac{22}{7} \times \frac{7}{2}(14 + \frac{7}{2} )$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf \frac {\cancel{22}}{ \cancel7} \times \frac{ \cancel7}{ \cancel2} \times \frac{28 + 7}{2}$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf 11 \times \frac{28 + 7}{2}$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf 11 \times \frac{35}{2}$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf \frac{11 \times 35}{2}$

$\small \sf \:: \longrightarrow Total \: Surface \: Area \: of \: the \: Cone \large \leadsto \small \bf 192.5 \: cm {}^{2}$

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$\underline{ \sf \: More \: Information:-}$

• $\small \sf \: Curved \: Surface \: Area \: of \: a \: Cone \large\leadsto \small \boxed{ \bf \pi rl}$

• $\small \sf \: Total \: Surface \: Area \: of \: a \: Cone \large\leadsto \small \boxed{ \bf \pi r(r + l)}$

• $\small \sf \: \: Surface \: Area \: of \: a \: Sphere \large\leadsto \small \boxed{ \bf4 \pi r {}^{2} }$

• $\small \sf \: Total \: Surface \: Area \: of \: a \: Hemisphere \large\leadsto \small \boxed{ \bf 3\pi r {}^{2} }$

• $\small \sf \: Curved \: Surface \: Area \: of \: a \: Hemisphere\large\leadsto \small \boxed{ \bf2 \pi r {}^{2} }$

• $\small \sf \: Volume \: of \: a \: Cuboid \large\leadsto \small \boxed{ \bf l \times b \times h}$

• $\small \sf \: Volume \: of \: a \: Cube \large\leadsto \small \boxed{ \bf {a}^{3} }$

• $\small \sf \: Volume \: of \: a \: Cylinder \large\leadsto \small \boxed{ \bf \pi {r}^{2}h }$

• $\small \sf \: Volume \: of \: a \:Cone\large\leadsto \small \boxed{ \bf \frac{1}{3}\pi r {}^{2} h }$

• $\small \sf \: Volume \: of \: a \: Sphere \large\leadsto \small \boxed{ \bf \frac{4}{3} \pi r {}^{3} }$

• $\small \sf \: Volume \: of \: a \: Hemisphere \large\leadsto \small \boxed{ \bf \frac{2}{3}\pi {r}^{3} }$

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