Question

If the radius of the base and height of a cone are "a" and " 2a"
respectively, then its curved surface area is ?​

Answer 1

Given :

➝ Radius of cone = a

➝ Height of cone = 2a

To find :

➝ Curved surface area (C.S.A) of cone

Formula used :

➝ l² = r² + h²

➝ C.S.A = π r l

Where :-

l = slant height

r = radius of base of cone

h = height of cone

C.S.A = Curved surface area

Solution :

➝ Radius of base of cone = a

➝ Height of cone = 2a

Now , we have to find out slant height of cone.

➝ l² = a² + (2a)²

➝ l² = a² + 4a²

➝ l² = 5a²

➝ l = √(5a²)

➝ l = √(5) a

Slant height = a√5 units

Now , we will find out C.S.A :-

➝ C.S.A = π × a× √(5) a

➝ C.S.A = π√(5) a² square unit

Answer :

π√(5) a² square unit

Answer 2

Step-by-step explanation:

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$\text{\huge\underline{\red{Question:-}}}$

:$\Longrightarrow$ ● If the radius of the base and height of a cone are "a" and " 2a" respectively, then its curved surface area is ?

$\text{\huge\underline{\orange{To\ Find:-}}}$

:$\Longrightarrow$ ● We have to find the curved surface area of cone.

$\text{\huge\underline{\green{Given:-}}}$

:$\Longrightarrow$ ● Radius of cone = a.

:$\Longrightarrow$ ● Height of cone = 2a.

$\text{\large\underline{\blue{Formula\ to\ be\ used:-}}}$

:$\Longrightarrow$ $\mathrm\orange{l²\ =\ r²\ +\ h².}$

:$\Longrightarrow$ $\mathrm\orange{C.S.A\ =\ \pi\ r\ l.}$

$\text{\large\underline{\bf{And\ Where:-}}}$

:$\Longrightarrow$ $\mathrm\orange{l\ =\ slant\ height.}$

:$\Longrightarrow$ $\mathrm\orange{r\ =\ radius\ of\ base\ of\ cone.}$

:$\Longrightarrow$ $\mathrm\orange{h\ =\ height\ of\ cone.}$

:$\Longrightarrow$ $\mathrm\orange{C.S.A\ =\ Curved\ Surface\ Area.}$

$\text{\Large\underline{\purple{Now,\ Solution:-}}}$

:$\Longrightarrow$ $\mathrm{Radius\ of\ base\ of\ cone\ =\ a}$

:$\Longrightarrow$ $\mathrm{Height\ of\ cone\ =\ 2a}$

$\mathrm\pink{We\ have\ to\ find\ the\ slant\ height\ of\ the\ cone:-}$

:$\Longrightarrow$ $\mathrm{l²\ =\ a²\ +\ (2a)²}$

:$\Longrightarrow$ $\mathrm{l²\ =\ a²\ +\ 4a²}$

:$\Longrightarrow$ $\mathrm{l²\ =\ 5a²}$

:$\Longrightarrow$ $\mathrm{l\ =\ \sqrt{(5a²)}}$

:$\Longrightarrow$ $\mathrm{l\ =\ \sqrt{(5)}\ a}$

:$\Longrightarrow$ $\mathrm{Slant\ height\ =\ a\ \sqrt{5}\ units.}$

$\text{\large\underline{\bf{Now,\ we\ will\ find\ C.S.A:-}}}$

:$\Longrightarrow$ $\mathrm{C.S.A\ =\ \pi\ ×\ a\ ×\ \sqrt{(5)}\ a}$

:$\Longrightarrow$ $\mathrm{C.S.A\ =\ \pi\ \sqrt{(5)}\ a²\ square\ unit.}$

:$\Longrightarrow$ $\mathrm\purple{Hence,\ the\ answer\ is\ \pi\ \sqrt{(5)}\ a²\ square\ unit.}$

$\text{\huge\underline{\bf{Hence\ Verified}}}$

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