Question

The volume of a right circular cone is 9856cm3 and the area of its base is 616cm2.Find:(i)the slant height of the cone. (ii)total surface area of the cone.

Answer 1

hello users ........

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 

now
(1) slant height of the cone =√ ( r² + h²) = √ ( 14² + 48² )
= √ ( 196 +2304 ) = √2500 = 50 cm answer

(2) surface area of cone =πr{r + l) }
= πr² + πrl = 616 + 3.14 × 14 × 50  = 616 + 2198 = 2814 cm² answer 

✪✪ hope it helps ✪✪

Answer 2

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 

now

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

= √ ( 14² + 48² )

= √ ( 196 +2304 )

= √2500

= 50 cm answer

(2) surface area of cone          =   πr{r + l) }

= πr² + πrl

= 616 + 3.14 × 14 × 50  

= 616 + 2198

= 2814 cm² answer