Question

C.S.A of cone is 308 sq cm and its slant height is 14 cm. (1) Radius (2) Total surface area of
cone​

Answer 1

$\red{\large {\pmb{\rm{\leadsto \: Given:}}}}$

Given that :

• CSA of cone = 308cm²

• Slant height (l) = 14cm

$\red{\large {\pmb{\rm{\leadsto \: To \: find:}}}}$

We have to find :

• The radius

• TSA of cone

$\red{\large{\pmb{\rm{\leadsto \: Solution:}}}}$

• Finding radius :

$\dag \: \: {\red{\pmb{\sf{CSA \: of \: cone=\pi rl}}}} \: \: \dag$

$:\implies \sf \pi rl=308cm^2$

$:\implies \sf \cfrac{22}{7} \: r \: (14cm) =308cm^2$

$:\implies \sf \cfrac{22}{\cancel7} \: r \: (\cancel{14cm})=308cm^2$

$: \implies\sf22 \times 2 \times r = 308 {cm}^{2}$

$:\implies \sf 44r= 308cm^2$

$:\implies \sf r= \cfrac{308}{44}$

${\green{\pmb{\sf {\therefore \: r=7cm}}}}$

• Finding TSA of cone by taking r=7cm :

$\dag \: \: {\red{\pmb{\sf{TSA \: of \: cone=\pi r(r + l)}}}} \: \: \dag$

$:\implies \sf \cfrac{22}{7} \: (7cm)(7cm+14cm)$

$:\implies \sf \cfrac{22}{\cancel7} (\cancel{7cm})(28cm)$

$:\implies \sf 22 \times 28cm$

${\green{\pmb{\sf{\therefore \: TSA \: of \: cone=616cm^2}}}}$

$\red{\large {\pmb{\rm{\leadsto~Know~more:}}}}$

• CSA of cube : 4a²

• TSA of cube : 6a²

• Volume of cube : a³

• TSA of hemisphere : 2πr²

• CSA of hemisphere : 3πr²

• Volume of cuboid : lbh

• CSA of cuboid : 2h(l+b)

Answer 2

Step-by-step explanation:

⇝Given:

⇝Given:

Given that :

CSA of cone = 308cm²

Slant height (l) = 14cm

\begin{gathered} \\ \end{gathered}

\red{\large {\pmb{\rm{\leadsto \: To \: find:}}}}

⇝Tofind:

⇝Tofind:

We have to find :

The radius

TSA of cone

\begin{gathered} \\ \end{gathered}

\red{\large{\pmb{\rm{\leadsto \: Solution:}}}}

⇝Solution:

⇝Solution:

Finding radius :

\dag \: \: {\red{\pmb{\sf{CSA \: of \: cone=\pi rl}}}} \: \: \dag†

CSAofcone=πrl

CSAofcone=πrl†

:\implies \sf \pi rl=308cm^2:⟹πrl=308cm

2

:\implies \sf \cfrac{22}{7} \: r \: (14cm) =308cm^2:⟹

7

22

r(14cm)=308cm

2

:\implies \sf \cfrac{22}{\cancel7} \: r \: (\cancel{14cm})=308cm^2:⟹

7

22

r(

14cm

)=308cm

2

: \implies\sf22 \times 2 \times r = 308 {cm}^{2}:⟹22×2×r=308cm

2

:\implies \sf 44r= 308cm^2:⟹44r=308cm

2

:\implies \sf r= \cfrac{308}{44}:⟹r=

44

308

{\green{\pmb{\sf {\therefore \: r=7cm}}}}

∴r=7cm

∴r=7cm

Finding TSA of cone by taking r=7cm :

\dag \: \: {\red{\pmb{\sf{TSA \: of \: cone=\pi r(r + l)}}}} \: \: \dag†

TSAofcone=πr(r+l)

TSAofcone=πr(r+l)†

:\implies \sf \cfrac{22}{7} \: (7cm)(7cm+14cm):⟹

7

22

(7cm)(7cm+14cm)

:\implies \sf \cfrac{22}{\cancel7} (\cancel{7cm})(28cm):⟹

7

22

(

7cm

)(28cm)

:\implies \sf 22 \times 28cm:⟹22×28cm

{\green{\pmb{\sf{\therefore \: TSA \: of \: cone=616cm^2}}}}

∴TSAofcone=616cm

2

∴TSAofcone=616cm

2

\begin{gathered} \\ \end{gathered}

\red{\large {\pmb{\rm{\leadsto~Know~more:}}}}

⇝ Know more:

⇝ Know more:

CSA of cube : 4a²

TSA of cube : 6a²

Volume of cube : a³

TSA of hemisphere : 2πr²

CSA of hemisphere : 3πr²

Volume of cuboid : lbh

CSA of cuboid : 2h(l+b)

\begin{gathered}\\\end{gathered}