Question

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π =3.14)

Answer 1

Answer:

Radius of the base (r) = 10cm

Slant height (l) = 26 cm

Explanation:

Given:

The radius and the height of a right circular cone are in the ratio 5 : 12 and volume is 2512 cm³ and π = 3.14

To find:

i) Radius of the base (r)

ii) slant height(l)

Explanation:

i)Ratio of radius and height

= r : h = 5:12

Let r = 5x and h = 12x

We know that,

Volume of a cone = 2512 cm³

Therefore,

$x = 2$

Now ,

Radius (r) =5x = 5×2 = 10cm

Height (h) = 12x =12×2 = 24cm

ii) we know that,

=> l = √(10)²+(24)²

=> l = √100+576

=> l = √676

=> l = √(26)²

=> l = 26 cm

Therefore,

Radius of the base (r) = 10cm

Slant height (l) = 26 cm

Answer 2

Answer:

The slant height of cone is 26 cm

The radius of cone is 10 cm  

Step-by-step explanation:

Given as :

The ratio of radius and height of right circular cone = 5 : 12

Let The radius of cone = r = 5 x   cm

Let The height of cone = h = 12 x   cm

The volume of cone = 2512 cubic cm

Let The slant height of cone = l cm

According to question

∵ volume of cone = $\dfrac{1}{3}$ × π × r² × h

where r is radius

          h is height

Or,  $\dfrac{1}{3}$ × π × r² × h = 2512

or, 3.14 × r² × h = 2512 × 3

Or, 3.14 × (5 x)² × (12 x) = 7536

Or, 942 x³ = 7536

Or, x³  =  $\dfrac{7536}{942}$

Or,  x³ = 8

∴  x = ∛8 = 2

So, The radius of cone = r = 5 × 2 = 10 cm

The height of cone = h = 12 × 2 = 24  cm

And

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

i.e  l = $\sqrt{10^{2}+24^{2} }$

∴   slant height = √676 = 26 cm

So, The slant height of cone = l = 26 cm

Hence, The slant height of cone is 26 cm

And The radius of cone is 10 cm  Answer