Question

The radius and the height of right circular cone are in the ratio 5 : 12 and its volume is 314m^3 then find the slant height.

Answer 1

the radius and height of a right circular cone are in the ratio 5:12 if its volume is 314cm find the slant height and curved surface area

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Radius be r

Height be h

Ratio = 5p and 12p respectively

${\boxed{\sf\:{Volume\;of\;Cone}}}$

$\tt{\rightarrow\dfrac{1}{3}\times\pi r^2h}$

$\tt{\rightarrow\dfrac{1}{3}\times 3.14\times(5p)^2\times 12p}$

= 3.14 × 25p² × 4p m³

= 314p³ m³

(Given)

Volume of Cone = 314 m³

314p³ = 314

$\tt{\rightarrow p^3=\dfrac{314}{314}}$

p = 1

Now,

$\textbf{\underline{Radius\;of\;Cone}}$

5p = 5(1) = 5

Now,

$\textbf{\underline{Slant\;Height}}$

l = √h² + r²

l = √(12)² + (5)²

l = √144 + 25

l = √169

l = 13 m

Therefore we get the values,

Slant height of cone = 13 m