Question

curved surface area of a cone is 308cm² and it's slant height is 14cm. find (i) radius of the base and (ii) total surface area of the cone​

Answer 1

Given:-

• C.S.A of cone =308cm²
• Slant height (l) =14 cm

To find out:-

• Radius of the base=?
• T.S.A of the cone=?

Formula used:-

• CSA of cone=πrl
• TSA of cone=πr(l+r)

Solution:-

CSA of cone =πrl

⇒πrl=308

⇒πr =308/l

⇒πr=308/14

⇒r=22×7/22

⇒r=7cm

Thus the radius of the base is 7cm.

⇒TSA of cone = πr(l+r)

⇒TSA of cone = π×7(7+14)

⇒TSA of cone = 22/7×7×21

⇒TSA of cone = 22×21

⇒TSA of cone = 462 cm²

_____________________

Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Given :}}}}}}\end{gathered}$

• ↠ Curved surface area of a cone = 308 cm².
• ↠ Height of cone = 14cm

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:To Find :}}}}}}\end{gathered}$

• ↠ (i) Radius of the base
• ↠ (ii) Total surface area of the cone

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Using Formulae :}}}}}}\end{gathered}$

$\bigstar{\underline{\boxed{\bf{\red{Curved \: surface \: area \: of \: cone = \pi rl}}}}}$

$\bigstar{\underline{\boxed{\bf{\red{Total \: surface \: area \: of \: cone = \pi r(r + l)}}}}}$

Where

• ↠ r = radius
• ↠ l = slant height of the cone
• ↠ π = 22/7

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Solution :}}}}}}\end{gathered}$

Here

• ↠ C.S.A of cone = 308 cm².
• ↠ Height of cone = 14 cm
• π = 22/7

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

(i) Finding, the radius of base

${\dashrightarrow{\pmb{\sf{Curved \: surface \: area \: of \: cone = \pi rl}}}}$

• Substuting the values

${\dashrightarrow{\sf{308 \: {cm}^{2} = \dfrac{22}{7} \times r\times 14}}}$

${\dashrightarrow{\sf{308 \: {cm}^{2} = \dfrac{22}{\cancel{7}} \times r\times \cancel{14}}}}$

${\dashrightarrow{\sf{308 \: {cm}^{2} = 22\times r\times2}}}$

${\dashrightarrow{\sf{308 \: {cm}^{2} = 44r}}}$

${\dashrightarrow{\sf{Radius = \dfrac{308}{44}}}}$

${\dashrightarrow{\sf{Radius = \cancel{\dfrac{308}{44}}}}}$

${\dashrightarrow{\sf{Radius = 7 \: cm}}}$

$\bigstar{\underline{\boxed{\bf{\green{Radius \: of \: the \: base = 7 \: cm}}}}}$

∴ The radius of base is 7 cm.

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

(ii) Finding, Total surface area of the cone

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

• Substuting the values

${\dashrightarrow{\sf{Total \: surface \: area \: of \: cone = \dfrac{22}{7} \times 7(7 + 14)}}}$

${\dashrightarrow{\sf{Total \: surface \: area \: of \: cone = \dfrac{22}{\cancel{7}} \times \cancel{7}(21)}}}$

${\dashrightarrow{\sf{Total \: surface \: area \: of \: cone = 22 \times 21}}}$

${\dashrightarrow{\sf{Total \: surface \: area \: of \: cone = 462 \: {cm}^{2}}}}$

$\bigstar{\underline{\boxed{\bf{\green{Total \: surface \: area \: of \: cone = 462 \: {cm}^{2}}}}}}$

∴ The total surface area of cone is 462 cm².

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Answer :}}}}}}\end{gathered}$

• ↠ The radius of base is 7 cm.
• ↠ The total surface area of cone is 462 cm².

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Diagram :}}}}}}\end{gathered}$

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{7\ cm}}\put(9.5,10){\sf{14\ cm}}\end{picture}$

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Additional Information :}}}}}}\end{gathered}$

⟶ Volume of cylinder = πr²h

⟶ T.S.A of cylinder = 2πrh + 2πr²

⟶ Volume of cone = ⅓ πr²h

⟶ C.S.A of cone = πrl

⟶ T.S.A of cone = πrl + πr²

⟶ Volume of cuboid = l × b × h

⟶ C.S.A of cuboid = 2(l + b)h

⟶ T.S.A of cuboid = 2(lb + bh + lh)

⟶ C.S.A of cube = 4a²

⟶ T.S.A of cube = 6a²

⟶ Volume of cube = a³

⟶ Volume of sphere = 4/3πr³

⟶ Surface area of sphere = 4πr²

⟶ Volume of hemisphere = ⅔ πr³

⟶ C.S.A of hemisphere = 2πr²

⟶ T.S.A of hemisphere = 3πr²

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

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Request :}}}}}}\end{gathered}$

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