Question

Calculate the total surface area and curved surface area of a cone of which slant height is 28 m and radius is 7m.​

Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 28m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 7m$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: (i) \: Total \: surface \: area \: of \: cone \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cone$

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: Total \: surface \: area = \pi rl + \pi {r}^{2} \\ \\ \sf \: Curved \: surface \: area = \pi rl$

$\large{\red{\bold{\underline{Solution:}}}}$

$\sf \: Let's \: consider \: total \: surface \: area \: as \: T.S.A. \\ \sf \: And \: curved \: surface \: area \: as \: C.S.A.$

$\large{\pink{\bold{\underline{Then:}}}}$

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(7 + 28) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(35) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel7 (35) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 35 \\ \\ \longrightarrow \: \sf \:T.S.A = 770 \: {m}^{2}$

$\large{\green{\bold{\underline{And:}}}}$

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 7 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel7 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = 616 \: {m}^{2}$

$\large{\red{\bold{\underline{Therefore:}}}}$

$\sf \: Total \: surface \: area \: of \: cone \: is \: 770 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 616 {m}^{2}.$

Answer 2

$\huge\underline\mathbb{\red Q\pink{U}\purple{ES} \blue{T} \orange{IO}\green{N :}}$

Calculate the total surface area and curved surface area of a cone of which slant height is 28 m and radius is 7m.

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

★ Given that,

• $\bf\: ↪Slant\:height(l)\:_{(Cone)} = 28 m.$
• $\bf\:↪ Radius(r)\:_{(Cone)} = 7 m.$

★ To find,

• $\bf\red{ Total\:surface\:area\:_{(Cone)}}$
• $\bf\red{ Curved\:surface\:area\:_{(Cone)}}$

★ We know that,

Formal for :

$\sf\:\implies Total\:surface\:area\:_{(Cone)} = tex\pir(r + l)$

$\sf\: \implies \frac{22}{7} \times 7(7 + 28)$

$\sf\:\implies 22(35)$

$\sf\:\implies 770$

$\underline{\boxed{\bf{\purple{ ∴ Hence, \:Total\:surface\:area\:of\:cone\: = 770 m^{2}}}}}\:\blue{\bigstar}$

Formula for :

$\sf\:\implies Curved\:surface\:area\:_{(Cone)} = \pirl$

$\sf\:\implies \frac{22}{7} \times 7 \times 28$

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

$\sf\:\implies 616$

$\underline{\boxed{\bf{\purple{ ∴ Hence, \:Curved\:surface\:area\:of\:cone\: = 616 m^{2}}}}}\:\blue{\bigstar}$

Hence, it is solved....

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★ Cone Formulas :

$\tt\green{ ◼ \: Total\:surface\:area\:_{(Cone)} : \pir(r + l) }$

$\tt\green{ ◼ \: Curved\:surface\:area\:_{(Cone)} : \pirl }$

$\tt\green{ ◼ \: Volume\:_{(Cone)} : \frac{1}{3}\:\pir²h}$

$\tt\green{ ◼ \: Slant\:height\:_{(Cone)} : l = \sqrt{h² + r²}}$

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