Question

The curved surface area of the cone with height 6cm and slant height 10 cm is(π=3.14)​

Answer 1

Given :

• Height of a cone = 6 cm
• Slant height = 10 cm
• π = 3.14

To Find :

• The Curved surface area of the cone

Solution :

The relation between Radius , slant height and height of a cone is given by ,

$\\ \star \: {\boxed{\purple{\sf{ {l}^{2} = {r}^{2} + {h}^{2} }}}}$

$\\ \sf{we \: have}\begin{cases} &\sf{slant \: height(l) = 10 \: cm} \\ & \sf{height \: (h) \: =6 \: cm } \end{cases}$

Substituting the values ,

$\\ : \implies \sf \: {(10 \: cm)}^{2} = {r}^{2} + {(6 \: cm)}^{2}$

$\\ : \implies \sf \: 100 \: cm {}^{2} = {r}^{2} + 36 \: {cm}^{2}$

$\\ : \implies \sf \: 100 \: {cm}^{2} - 36 \: {cm}^{2} = {r}^{2}$

$\\ : \implies \sf \: {r}^{2} = 64 \: {cm}^{2}$

$\\ : \implies \sf \: r = \sqrt{64 \: {cm}^{2} }$

$\\ : \implies{\boxed{\red{\mathfrak{r = 8 \: cm}}}}$

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Now CSA of a cone is given by ,

$\\ \star \: {\boxed{\purple{\sf{CSA = \pi rl}}}}$

Substituting the values we have ,

$\\ : \implies \sf \:CSA = (3.14)(8 \: cm)(10 \: cm)$

$\\ : \implies{\underline{\boxed{\pink{\sf{ \: CSA = 251.2 \: {cm}^{2} }}}}} \: \bigstar$

$\\ \therefore{\underline{\sf{Hence , \: The \: CSA \: of \: the \: cone \: is \: \bold{251.2 \: cm^2}}}}$

Answer 2

Answer:

Given :-

• A curved surface area of the cone whose height is 6 cm and slant height is 10 cm. (π = 3.14)

To Find :-

• What is the curved surface area of the cone

Formula Used :-

❶$\boxed{\bold{\large{l\: =\: \sqrt{{h}^{2} + {r}^{2}}}}}$

❷ $\boxed{\bold{\large{C.S.A\: of\: cone\: =\: {\pi}rl}}}$

Solution :-

❶ First, we have to find the radius,

Given :

• Height = 6 cm
• Slant height = 10 cm

According to the question by using the formula we get,

⇒ (l)² = (h)² + (r)²

⇒ (10)² = (6)² + (r)²

⇒ 100 = 36 + r²

⇒ r² = 100 - 36

⇒ r² = 64

⇒ r = $\sqrt{64}$

➠ r = 8 cm

Hence, we get the value of radius is 8 cm.

❷ Now, we have to find the value of CSA of cone,

We get,

• Radius = 8 cm
• Slant height = 10 cm
• π = 3.14

According to the question by using the formula we get,

↦ C.S.A = 3.14 × 8 × 10

↦ CSA = 25.12 × 10

➥ CSA = 251.2 cm²

$\therefore$ The CSA of the cone is 251.2 cm² .