The radius and height of a right circular cone are in the ratio 2 : 3. Find the slant height if its volume is 100.48 cu.cm. ( Take π = 3.14)

GIVEN : radius of cone = ”r”

Height of cone = “h”

=

Volume of the cone = 100.48 cu.cm

We take π = 3.14

TO FIND : slant height “l” = ?

PROCEDURE :

We know that volume of the cone “V” = × π r²h

Now =

⇒ r =

Now putting the values in the formula of volume, we get

V = × π r²h

100.48 = × 3.14 × ()² × h

100.48 = × 3.14 × × h³

h³ = 100.48 × 3 × ×

h³ = 32 × 3 × = 8× 27

h = ∛ 8× 27 = ∛ 2× 2× 2× 3× 3× 3

h = 2× 3 = 6cm

now, r = = = 4cm

now, slant height “l” can be found using :

l² = r² + h²

= 4² + 6² = 16 + 36 = 52

L = √ 52 = 2√13cm

∴ slant height of the given cone is 2√13cm.