Question

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

Answer 1

Answer:

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Answer 2

Given:

$\begin{gathered} \sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 28m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 14m\end{gathered} </p><p>(i)Slantheightofthecone(l)=28m</p><p>(ii)Radiusofitsbase(r)=14m$

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

ToFind:

$\begin{gathered} \sf \: (i) \: Total \: surface \: area \: of \: cone \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cone \end{gathered}$

(i)Total surface area of cone

(ii)Curved surface area of cone

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

FormulaUsed:

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

Total surface area = πrl+πr

Curved surface area = πrl

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

Solution:

$\begin{gathered} \sf \: Let's \: consider \: total \: surface \: area \: as \: T.S.A. \\ \sf \: And \: curved \: surface \: area \: as \: C.S.A. \end{gathered}$

Let's consider total surface area as T.S.A.

And curved surface area as C.S.A.

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

Then:

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

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

And:

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

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

Therefore:

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