Question

curved surface of a cone is 308cm^2 and it's slant height is 13 cm. find (1) radius of the base and (2) total surface area of the cone. ​

Answer 1

Given :

• C.S.A of Cone is 308 cm² .
• Slant Height of Cone is 13 cm .

To Find :

• Radius of Cone .
• Total Surface Area of Cone .

Solution :

$\longmapsto\tt{Slant\:Height\:(l)=13\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{308=\dfrac{22}{7}\times{r}\times{13}}$

$\longmapsto\tt{308\times{7}=22\times{r}\times{13}}$

$\longmapsto\tt{2156=286\:{r}}$

$\longmapsto\tt{r=\cancel\dfrac{2156}{286}}$

$\longmapsto\tt\bf{r=7.5\:cm}$

Now ,

For Total Surface Area :

$\longmapsto\tt{Radius(r)=7.5\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{\dfrac{22}{7}\times{7.5}\times{(13+7.5)}}$

$\longmapsto\tt{\cancel\dfrac{165}{7}\times{20.5}}$

$\longmapsto\tt{23.5\times{20.5}}$

$\longmapsto\tt\bf{481.75\:{cm}^{2}\:(Approx.)}$

So , The Total Surface Area of Cone is 481.75 cm²(Approx.) ..

Answer 2

$\huge \bf \: Given$

➊CSA of cone = 308 cm²

➋Slant height = 13 cm

$\huge \bf \: To \: find$

Radius of the base

TSA

$\huge \bf \: Formula$

$\bf for \: radius \: of \: base \huge \boxed{\pi \: rl}$

$\bf \: for \: tsa \boxed {\pi r(l + r)}$

$\huge \bf \: Solution$

$\sf \: csa \: = \dfrac{22}{7} \times r \times 13$

$\sf \: 308 = \dfrac{22}{7} \times r \times 13$

$\sf \: 308 \times 7 = 22 \times r \times 13$

$\sf \: 2156 = 286$

$\huge \bf \: Radius \: = 7.5 \: cm$

Now,

Finding TSA of cone

$\sf \: tsa \: = \dfrac{22}{7} \times 7.5(13 + 7.5)$

$\sf \: tsa \: = \dfrac{165}{7} \times 20.5$

$\sf \: tsa \: = 23.5 \times 20.5$

$\huge \bf \: tsa \: = 481.75 \: cm$