Question

GIVEN:-
•CONE'S RADIUS= 9cm.
•VERTICAL HEIGHT =16cm.
FIND:-
•VOLUME OF CONE.
•CSA OF CONE.

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•NEED PROPER ANSWER.
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Answer 1

Question :-

Given above ↑

Answer :-

$(1) \: \mapsto \blue{ \boxed{\sf \pink{TSA = 9 \pi \sqrt{337}} + 81 \pi}} \\ \\ \bf or \: \\ \mapsto \boxed{ \orange{\sf \: v = 9 \pi( \sqrt{337}} + 9)} \\ \\ (2) \mapsto \red{ \boxed{ \sf \green{ CSA = \: 9 \pi \sqrt{337}} }} \\ \\ (3) Volume = 432 \pi \:$

To Find :-

(1) Total surface area

(2) Curved surface area (CSA) of cone .

(3) Volume

Solution :-

Given that :

• radius of its base (r) = 9 cm

• vertical height (h) = 16 cm

Firstly we will have to find slant height (l )of this cone

$\because \sf \red{ slant \: height \: (l)} = \green{ \sqrt{ {r}^{2} + {h}^{2} } } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ {(9)}^{2} + {(16)}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \blue{ \sqrt{81 + 256} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: l = \sqrt{337}$

Now ,we know that

(2) Curved surface area of cone = πrl

$\mapsto \red{ \boxed{ \sf \green{ CSA = \: 9 \pi \sqrt{337}} }}$

(1) now ,

$\mapsto \sf total \:surface \: area \: (TSA) = CSA + \pi {r}^{2} \\ \\ \sf \mapsto \: TSA = 9 \pi \sqrt{337} + \pi \: {(9)}^{2} \\ \\ \mapsto \blue{ \boxed{\sf \pink{TSA= 9 \pi \sqrt{337}} + 81 \pi}} \\ \\ \bf or \: \\ \\ \mapsto \boxed{ \orange{\sf \: TSA = 9 \pi( \sqrt{337}} + 9)}$

(3) Volume of cone

→ Now ,volume of cone

→ 1/3 πr² h

→ 1/3 π (9)² × 16

→ (81×16 × π)/3

→ 432 π

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt\bf{Given}}\begin{cases}\sf{Radii\:of\:cone = 9\:cm}\\\sf{Vertical\:height\:of\:cone=16\:cm} \end{cases}$

${\huge\tt\bf{To\:Find}}\begin{cases}\sf{Volume\:of\:cone=?}\\\sf{CSA\:of\:cone=?} \end{cases}$

$\huge\tt\bf {Solution:-}$

Volume of cone :-

$\huge {\boxed {\tt\dfrac {1}{3}\pi {r}^{2} h}}$

Putting in the given values,

$\leadsto\tt{\dfrac {1 }{3}\times \dfrac {22}{7}\times {(9)}^{2}\times 16}$

$\huge\leadsto \tt {\underline{1,357.7142\: {cm}^{3}}}$

CSA of cone:-

$\huge {\boxed {\tt \pi r l}}$

Let's find l,

$\huge {\boxed {\tt l =\sqrt {{h}^{2}+{r}^{2}}}}$

$\leadsto\tt {l= \sqrt{{(16)}^{2}+{(9)}^{2}}}$

$\leadsto\tt{l=\sqrt {337}}$

$\leadsto \tt {l=18.35\:cm}$

Now finding CSA,

$\leadsto \tt {\dfrac {22}{7}\times 9\times 18.35}$

$\huge\leadsto \tt {\underline{519.042\:{cm}^{2}}}$

$\rule {200}2$