Question

Find the curved and total surface area of the cone whose height is 8 cm and radius of base is 6 cm

Answer 1

Given :

• Height = 8cm
• Radius = 6cm

To Find :

• C.S.A of Cone
• T.S.A of Cone

Solution :

Firstly we will find the slant height of cone :

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

$\longrightarrow\tt{{l}^{2}=\sqrt{{(8)}^{2}+{(6)}^{2}}}$

$\longrightarrow\tt{{l}^{2}=\sqrt{64+36}}$

$\longrightarrow\tt{{l}^{2}=\sqrt{100}}$

$\longrightarrow\tt\bold{l=10cm}$

So , The slant height (l) of Cone is 10cm...

Now :

$\longrightarrow\tt{Slant\:height(l)=10cm}$

$\longrightarrow\tt{Radius(r)=6cm}$

Using Formula :

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

Putting Values :

$\longrightarrow\tt{\dfrac{22}{7}\times{6}\times{10}}$

$\longrightarrow\tt{\cancel\dfrac{1320}{7}}$

$\longrightarrow\tt\bold{188.5{cm}^{2}\:(Approx.)}$

So , C.S.A of Cone is 188.5 cm²..

_____________________

Using Formula :

$\longrightarrow\tt\boxed{T.S.A\:of\:Cone=\pi{rl}+\pi{{r}^{2}}}$

Putting Values :

$\longrightarrow\tt{\dfrac{22}{7}\times{6}\times{10}+\dfrac{22}{7}\times{6}\times{6}}$

$\longrightarrow\tt{\dfrac{1320}{7}+\dfrac{792}{7}}$

$\longrightarrow\tt{\cancel\dfrac{2112}{7}}$

$\longrightarrow\tt\bold{301.7{cm}^{2}\:(Approx.)}$

So , T.S.A of Cone is 301.7cm²..