Question

the curved surface area of a cone is 308 CM square and its slant height is 14 cm find the radius of the base and total surface area of the cone

Answer 1

Step-by-step explanation:

the answer is given in the attachment.

Answer 2

Given :-

• C S A of cone = 308 cm²

• Slant height of cone = 14 cm

To find :-

• Radius of base = ?

• T S A of cone = ?

Solution :-

let the radius of base of cone be r cm.

$\bigstar{\underline{\boxed{\bf\red{C\:S\:A\:of\:cone=\pi{r}l}}}}$

$\rm\longrightarrow\:308=\dfrac{22}{\cancel{7}}\times\:r\times\:\cancel{14}\:\:\:\:\:2$

$\rm\longrightarrow\:308=44r$

$\rm\longrightarrow\:r=\cancel\dfrac{308}{44}$

$\rm\longrightarrow\:r=7\:cm$

Now,

$\bigstar{\underline{\boxed{\bf\pink{T\:S\:A\:of\:cone=\pi{r}(r+l)}}}}$

$\rm\:T\:S\:A\:of\:cone=\dfrac{22}{\cancel{7}}\times\:\cancel{7}\:(7+14)\:{cm}^{2}$

$\rm\:T\:S\:A\:of\:cone=22\times\:21\:{cm}^{2}$

$\rm\:T\:S\:A\:of\:cone=462\:{cm}^{2}$

hence,the radius of base will be 7cm and total surface area of cone will be 462 cm².