Question

Find
(i) the slant height of the cone.
(ii) total surface area
if

The volume of a right circular cone is 9856 cm3 and the area of its base is616​

Answer 1

............... ......

Answer 2

Answer:

Step-by-step explanation:

(i) the slant height of the cone - l =$r^{2} + h^{2}$

(ii) total surface area  - π r 2 + π L r

if   the volume of a right circular cone is $9856cm^{2}$ and the area of its base is 616​.

we have given 

 volume of the cone = 9856 cm³

and area of its base is = 616 cm²

we have to find 

(1) slant height if the cone = ? 

(2) total surface area of the cone = ? 

solution :-

we know that 

slant height (l) of the cone = √ ( r² + h²)

volume of cone = πr²h/3

and 

surface area of cone = πr{r + l }

now

given that 

area of its base is = 616 cm²

=> πr² = 616

=> r² = 616 / π

=> r² =196.178 

=> r = 14.01 ≈ 14 cm

also 

volume of cone = 9856 cm³

=>  πr²h/3 = 9856 cm³

=>  π × 616 / π × h = 9856 ×3

=>  h = 48 cm 

Slant height = $\sqrt{r^{2} + h^{2} }$

                    =$\sqrt{14^{2} + 48^{2} }$

                   = $\sqrt{2500}$ = 50 cm

∴ Slant Height = 50cm.

Total surface area =  $\pi r^{2} +\pi l r$

                              = $\frac{22}{7}$ * $14^{2}$ + $\frac{22}{7}$ * 50 * 14

                              = $\frac{22}{7}$ * 14*14 + 22*50*2

                              = 22 *14*2  + 22*50*2

                              = 616 + 2200

                              =  $2816cm^{2}$

Hope this helps you friend.