Question

The radii of circular ends of a bucket of height 24 cm are 15 cm and 5 cm. Find the area of its curved surface.

Answer 1

Radius of top of the bucket ( R ) = 15 cm.


Radius of bottom of the bucket ( r ) = 5 cm.


And


Height of the bucket ( H ) = 24 cm.





Therefore,


Slant Height ( L ) = √ ( H )² + ( R - r )²



=> ✓ ( 24)² + ( 15 - 5 )²



=> √576 + (10)²



=> √ 576 + 100


=> √676



=> 26 cm.

• Curved Surface area of bucket = πL ( R + r ) cm².



=> 22/7 × 26 ( 15 + 5 ) cm².




=> ( 22 × 26 ) × 20 / 7 cm².



=> ( 22 × 26 × 20 ) / 7 cm².




=> 1634.28 cm².

Answer 2

Given:

Height = 24 cm

Radius 1 = 5 cm

Radius 2 = 15 cm

To find:

Curved surface area.

Solution:

By formula,

Curved surface area = π * Length * ( Radius 1 + Radius 2 )

Here,

Length = √ ( Height + (  Radius 2 - Radius 1 )^2 )

Substituting,

√ ( 24 + ( 15 - 5 )^2 )

Length = 11 cm

Hence,

3.14 * 11 * ( 15 + 5 )

Curved surface area = 690 sq.cm

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