Question

You have to calculate the total surface area & curved surface area of a cone if it's radius is 14m & slant height is 28 m.​

Answer 1

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

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 28m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 14m$

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

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

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

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

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

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

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

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 14(14 + 28) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 14(42) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel14(42) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 2 \times 42 \\ \\ \longrightarrow \: \sf \:T.S.A = 1848 \: {m}^{2}$

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

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 14 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel14 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 2 \times 28 \\ \\ \longrightarrow \: \sf \: C.S.A = 1232 \: {m}^{2}$

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

$\sf \: Total \: surface \: area \: of \: cone \: is \: 1848 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 1232 {m}^{2}.$

Answer 2

$\sf{ \purple{\Large{Given:}}}$

◎ Radius of its circular base i.e., r = 14 m

◎ Slant height of a cone i.e., l = 28 m

$\sf{ \purple{\Large{To \: Find}}}$

๑ Total surface area of a cone

๑ Curved surface area of a cone

$\sf{ \purple{\Large{Solution:}}}$

Now by using formula we will find both Total surface area and Curved surface area of a cone.

Total Surface Area = Base Area + Curved Surface Area.

T.S.A = πr² + πrl

Formula for total surface area of a cone

$\underline{ \boxed{ \sf{T.S.A = \pi r(r + l)}}}$

Substituting the values in the formula, we have:

➩ $\sf{ T.S.A= \dfrac{22}{7} \times 14(14 + 28)}$

➩ $\sf{T.S.A = \dfrac{22}{7} \times 14(42)}$

➩ $\sf{T.S.A = \dfrac{22}{ \cancel 7} \times \cancel {14} \times 42}$

➩ $\sf{T.S.A = 22 \times 2 \times 42}$

➩ $\sf{T.S.A = 1848 \: {m}^{2} }$

∴ Total surface area of cone = ${ \green{\underline{ \boxed{ \sf{1848 \: {m}^{2} }}}}}$

Now,

Formula for calculating curved surface area of cone

$\underline{ \boxed{ \sf{Curved \: Surface \: Area = \pi rl }}}$

On Substituting the values in the formula, we have:

➩ $\sf{C.S.A = \dfrac{22}{7} \times 14 \times 28}$

➩ $\sf{C.S.A = \dfrac{22}{ \cancel7} \times \cancel 4} \times 28$

➩ $\sf{C.S.A = 22 \times 2 \times 28}$

➩ $\sf{C.S.A = 1232 \: {m}^{2} }$

∴ Curved surface area of cone = $\green{\underline{ \boxed{ \sf{1232 \: {m}^{2} }}}}$

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