Question

Curved surface area of a cone is 308cm and its slant height is 14cm find.(i) radius of the base (ii) Total surface area of the cone.

Answer 1

Given : -

• Curved Surface Area of Cone = 308cm²
• Slant Height = 14cm

To Find : -

• Radius of the Base
• Total Surface Area of Cone

Solution : -

$\longmapsto\tt{C.S.A\:of\:Cone={308cm}^{2}}$

$\longmapsto\tt{Slant\:Height\:(l)=14cm}$

Using Formula : -

$\longmapsto\tt{C.S.A\:of\:Cone=\pi{r}{l}}$

Putting Values : -

$\longmapsto\tt{308=\dfrac{22}{\cancel{7}}\times{r}\times{\cancel{14}}}$

$\longmapsto\tt{308=44r}$

$\longmapsto\tt{r=\cancel\dfrac{308}{44}}$

$\longmapsto\tt{r=7}$

Therefore , Radius of Base is 7cm ....

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(ii) Now : -

• Slant height (l) = 14cm
• Radius (r) = 7cm

Using Formula : -

$\longmapsto\tt{T.S.A\:of\:Cone=\pi{r}(l+r)}$

Putting Values : -

$\longmapsto\tt{\dfrac{22}{7}\times{7}\:(14+7)}$

$\longmapsto\tt{22\times{2}}$

$\longmapsto\tt{{462cm}^{2}}$

So , Total Surface Area of Cone is 462cm²

Answer 2

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