Question

the radius and the height of a right circular cone are in the ratio 5 : 12 and volume is 2512 cm cube find the slant height and the radius of the base of cone? Take Pi 3.14.

Answer 1

may be u understand.

Answer 2

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

$\frac{1}{3}\times \pi r^{2}h=2512$

$\implies \frac{1}{3}\times 3.14\times (5x)^{2}\times12x=2512$

$\implies 3.14\times 25x^{3}\times 4 = 2512$

$\implies 3.14\times100 x^{3} = 2512$

$\implies 314\times x^{3}= 2512$

$\implies x^{3}=\frac{2512}{314}$

$\implies x^{3} = 8$

$\implies x^{3} = 2^{3}$

Therefore,

$x = 2$

Now ,

Radius (r) =5x = 5×2 = 10cm

Height (h) = 12x =12×2 = 24cm

ii) we know that,

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

=> 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

•••