Question

An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use π = 22/7]

(A) 402.12 cm²

(B) 298 cm²

(C) 377.14 cm²

(D) 315 cm²

Answer 1

Option (C) is correct

Explanation

Height of the cone h=12cm

Radius of the cone r =9 cm

Slant height of the cone l=√(h^2+r^2)=15cm

Curved surface area of the conical pot will be S=π×r×l=135π cm^2

Let l' be the slant height occupied by water of depth h'=4cm

So l'/l=h'/h

=>l'=4/12×15=5cm

Hence radius of water cone 

r'=√(l'^2-h'^2)=√(5^2-4^2)=3cm

Curved surface area of water cone 

=π×r'×l'=15π

So area of interior surface of the cone not in contact with water will be

=(135-15)π cm^2=377.14 cm^2

Answer 2

The correct option is: (C) 377.14 cm²

Explanation:

Curved surface area of cone = πrl = 135 π

Slant height of conical part containing water

Curved surface area of conical part containing water = π r₁l₁ = 15π

Surface area of cone not in contact with water = 135 π - 15 π = 377.14 cm²