Question

the radius of a cone is 3cm and vertical height is 4cm.find the area of the curved surface
[ans. 62.85 cm^2]
solve and find the answer given below​

Answer 1

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$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• The radius of a cone is 3 cm and vertical height is 4cm. Find the CSA of the cone.

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$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{Radius of the cone = r = 3cm.}$

• $\textsf{Height of the cone = h = 4cm.}$

• $\textsf{Slant height of the cone = l = ?}$

• $\boxed{\sf{l = \sqrt{{r}^{2} + {h}^{2}}}}$

• $\sf{l = \sqrt{3^{2} + 4^{2} }}$

• $\sf{l = \sqrt{9 + 16}}$

• $\sf{l = \sqrt{25}}$

• $\textsf{l = 5cm}$

• $\boxed{\sf{CSA \:of\: cone = \pi rl}}$

• $\sf{\pi rl}$

• $\sf{\dfrac{22}{7} * 3 * 5}$

• $\textsf{3.14 * 15}$

• $\boxed{\sf{47.1 \:cm^{2}}}$

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$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf{CSA \: of \: cone \: = \: 47.1 \: {cm}^{2}.}}}$

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$\huge{\bf{\purple{\mathfrak{Extra \: Information:-}}}}$

• $\sf{CSA \: of \: cone \: = \pi rl \: {units}^{2}.}$

• $\sf{TSA \: of \: cone \: = \: \pi r(l \: + \: r) \: {units}^{2}.}$

• $\sf{Volume \: of \: cone\: = \dfrac{1}{3} \pi r^{2}h}$

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Answer 2

Answer:

Given :-

• Radius = 3 cm
• Height = 4 cm

To Find :-

CSA

Solution :-

At first we know that

CSA = πrl

But,

Slanght height isn't given. So, by using Pythagoras theorem.

Pythagoras theorem :- In this theorem a mathematician Pythagorean, discovered a new formula called Pythagoras theorem. In it the sum of squares of base and height is same as the square of Hypotenuse.

Here,

Hypotenuse = l

Base = r

Height = h

So,

By putting values

$\large \sf \: { \ell}^{2} = {3}^{2} + {4}^{2}$

$\sf \implies \ell {}^{2} = 9 + 16$

$\sf \implies { \ell}^{2} = 25$

$\sf \implies { \ell}= \sqrt{25}$

${ \frak {\red {\underline{ \ell \: = 5}}}}$

Now,

CSA = 22/7 × 3 × 5

CSA = 22/7 × 15

CSA = 47.1 cm²