Question

the diameter of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively if its height is 24 cm find the area of metal he used to make the bucket

Answer 1

Heya !!

Diameter of lower end = 10 cm
r = 10/2 = 5 cm

Diameter of upper end = 30 cm
R = 30/2 = 15 cm

Height = 24 cm

Slant height , l = √h²+(R²–r²)
=> √24²+(15²–5²)
=> √676
=> 26 cm

Area of metal sheet used = π ( r + R ) l + πr²
= 3.14 ( 5 + 15 ) 26 + 3.14 (5)²
= 3.14 ( 20 ) 26 + 3.14 ( 25 )
= 3.14 ( 520 ) + 3.14 ( 25 )
= 3.14 ( 520 + 25 )
= 3.14 × 545
= 1711.3 cm²

Answer 2

Given:

Diameter of the upper end = 30 cm

Diameter of the lower end = 10 cm

Height = 24 cm

To find:

Area

Solution:

Radius of the upper end of the cone = 15 cm

Radius of the lower end of the cone = 5 cm

In order to find the area,

The slant height should be calculated.

Slant height = √ ( h^2 + ( Radius of the upper end of the cone - Radius of the lower end of the cone )^2

√24^2 + ( 15 - 5 )^2  

√576 + 10^2

Slant height = 26 cm

Area of the metal  = Curved surface Area + Area of base of the cone.

Curved surface area = π ( Radius of the upper end of the cone - Radius of the lower end of the cone ) * Slant height

Area of the base = πr2^2

Hence,

π ( Radius of the upper end of the cone - Radius of the lower end of the cone ) * Slant height +  πr2^2

3.14 ( 15 + 5 ) × 26 + π( 5 )^2  

3.14 × 20 × 26 + 25 × 3.14

545 × 3.14

Area = 1711.3 sq.cm

Hence, the area of metal sheet used to make the bucket is 1711.3 sq.cm

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