Question

The ratio of the radius and height of a cone is 5 : 12, respectively. its volume is 314cc. find its slant height.

Answer 1

Hey !!

Here is your answer.... ⬇⬇⬇

Let radius and height of a cone is ( r ) and ( h ) respectively.

As given that ratio of radius and height is 5:12
so,

r/h = 5/12
h = 12r/5 ----- ( 1 )

Volume of cone is 314 cm^3

Volume = 314
1/3πr^2h = 314
1/3 × 31.4 × r^2 × 12r/5 = 314
12r^3 = 1500
r^3 = 1500/12
r^3 = 125
r = 5 cm

Put value of ( r ) in eq. ( 1 )..,

h = 12( 5 )/5
h = 60/5
h = 12 cm

Find slant height ( l )..,
l^2 = r^2 + h^2
l^2 = ( 5 )^2 + ( 12 )^2
l^2 = 25 + 144
l^2 = 169
l =√169
l = 13 cm

Slant height of cone is 13 cm.

HOPE IT HELPS YOU...

THANKS. ^-^

Answer 2

Hey friend, Harish here.

Here is your answer:

Given that:

Ratio of Radius (r) & Height (h) = 5 : 12

Volume of cone = 314 cm³.

To Find:

The slant height of the cone.

Solution:

Let radius (r) be 5x & Height(h) be 12x.

We know that,

$Volume\ of\ cone= \frac{1}{3} \pi r^{2}h$

⇒  $314 = \frac{1}{3}\times 3.14 \times (5x)^{2}\times (12x)$

⇒  $\frac{314}{3.14} = \frac{(5x)^{2}\times 12x}{3}$

⇒  $100 = 25x^{2} \times 4x$

⇒  $100 = 100x^{3}$

⇒  $x^{3} = \frac{100}{100} =1$

⇒  $x = 1$

Then,  Radius = 5 × x = 5 × 1 = 5 cm

           Height = 12 × x = 12 × 1 = 12cm

We know that,

$Slant\ height(l) = \sqrt{(h)^{2} +(r)^{2}} = \sqrt{(12)^{2} + (5)^{2}}$

 ⇒  [tex] \sqrt{144 +25 } = \sqrt{169} = 13\ cm [/tex]

Therefore the slant height is 13cm.
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Hope my answer is helpful to you.