Question

Total surface of a cone is 628cm^2 and slant height is 17cm. Find the radius? ​

Answer 1

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Answer 2

AnsWer :

Radius 25 Cm.

Given :

• TSA of Cone is 628 Cm²
• Slant height ( l ) is 17 Cm.

Formula :

$\tt\dagger \: \: \: \: \: TSA \: of \: Cone = \pi r(l + r)$

$\tt\dagger \: \: \: \: \: CSA \: of \: Cone = \pi rl.$

$\tt\dagger \: \: \: \: \: Volume \: of \: Cone =\dfrac{1}{3} \pi r^{2}h.$

Solution :

$\tt \longmapsto 628 = \pi r(l + r).$

$\tt \longmapsto 628 = \pi r(17 + r)$

$\tt \longmapsto \dfrac{628}{ \pi} = {r}^{2} + 17r$

$\tt \longmapsto \frac{628 }{3.14} = {r}^{2} + 17r.$

$\tt \longmapsto 200 = {r}^{2} + 17r.$

$\begin{array}{r | l} 2 & 200 \\ \cline{2-2} 2 & 100 \\ \cline{2-2} 2 & 50 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1 \end{array}$

$\tt\longmapsto {r}^{2} + 17r - 200 = 0.$

$\tt\longmapsto {r}^{2} - 25r + 8r - 200 = 0.$

$\tt\longmapsto r(r - 25) + 8(r - 25) = 0.$

$\tt \longmapsto (r + 8)(r - 25) = 0.$

$\rule{90}1$

Either,

$\tt \mapsto r + 8= 0.$

$\tt \mapsto r =-8.$

$\rule{40}1$

Or,

$\tt \mapsto r - 25= 0.$

$\tt \mapsto r = 25.$

$\rule{90}1$

Here, Ignore.

$\tt \mapsto \red{r \neq-8.}$

$\tt \red{Note : }The \: value \: of\: \pi = 3.14$

Therefore, the value of Radius of given Cone be 25 Cm.