Question

The volume of a right circular cone is 4710 cu cm .if the radius and height of the cone are in the ratio 3:4,find it's slant height ,when π3.14

Answer 1

$\Huge{\text{\underline{solution:-}}}$

Let the radius and Height be 3a and 4a respectively.

Volume = 4710

$\implies{\pi{\r^2{\frac{h}{3}}}}$ = 4710

$\implies$ 3.14 × (3a)³ × 4a = 4710 × 3

$\implies$ 3.14 × 36 a³ = 14130

$\implies$ a³ =$\frac{14130}{36}$ × 3.14

$\implies$ a³ = 125

$\implies$ $\boxed{\tt{a = 5}}$

Radius = 5 × 3 = 15 cm

Height = 5 × 4 = 20 cm

Slant Height = $\sqrt{( 15^2 + 20^2)}$

$\implies$ $\sqrt{(225 + 400)}$

$\implies$ $\sqrt{(625)}$

$\boxed{\tt{= 25 cm}}$

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Answer 2

$\huge{\underline{\underline{\mathrm{\red{Answer-}}}}}$

$\large{\underline{\boxed{\mathrm{\blue{Slant\:height\:of\:cone\:=\:25\:cm}}}}}$

$\huge{\underline{\underline{\mathrm{\red{Explanation-}}}}}$

Given :

• Volume of right circular cone = 4710 cm³
• Ratio of Radius and height of cone = 3 : 4

To find :

• Slant Height of right circular cone

Solution :

Let radius and height of cone be 3x and 4x respectively.

We know that,

$\large{\underline{\boxed{\rm{\green{Volume\:of\:cone\:=\:\dfrac{1}{3}\:\pi\:r^2\:h}}}}}$

Putting the values,

$\implies$ 4710 = $\dfrac{1}{3}$ × 3.14 × (3x)² × 4x

$\implies$ 36x³ × 3.14 = 4710 × 3

$\implies$ 36x³ = $\dfrac{4710\:\times\:3}{3.14}$

$\implies$ x³ = 125

$\implies$ x = $\sqrt[3]{125}$

$\rule{200}2$

Now, put x = 5 in 3x i.e radius.

$\implies$ Radius of cone = 3x

$\implies$ Radius of cone = 3 × 5

$\implies$ Radius of cone = 15 cm

Now put x = 5 in 4x i.e height.

$\implies$ Height of cone = 4x

$\implies$ Height of cone = 4 × 5

$\implies$ Height of cone = 20 cm

$\rule{200}2$

We also know that,

Slant Height of cone = $\sqrt{ {r}^{2} + {h}^{2} }$

Putting the values,

$\implies$ Slant height of cone = $\sqrt{ {15}^{2} + {20}^{2} }$

$\implies$ Slant height of cone = $\sqrt{ 225 + 400 }$

$\implies$ Slant height of cone = $\sqrt{625}$

$\large{\underline{\boxed{\mathrm{\blue{\therefore\:Slant\:height\:of\:cone\:=\:25\:cm}}}}}$