Question

The diameter of the lower and upper end of a bucket in the form of a frustum of a cone are10 cm and 30 cm respectively. If its height is 24 cm, find :i) the area of the metal sheet used to make the bucket.

Answer 1

Area of metal sheet to be used = CSA of Frustum + Area of base

                                                     = πl(R+r) + πr²

l = √h² + (R-r)²

l = √(24)² + (15-5)²

l = √576 + 100

l = √676 = 26 cm

Then,                                         = πl(R+r) + πr²

                                                  = 3.14 × 26 (15+5) + 3.14 (5)²

                                                  = 3.14 (26 × 20 + 25)  

                                                  = 3.14 (520 + 25)

                                                  = 3.14 × 525

                                                   = 1711.3 cm²
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Answer 2

Diameter of lower end (D1)

= 10 cm

Diameter of upper end (D2)

= 30 cm

Height of the bucket (h) = 24 cm

l^2 = (r2 - r1)^2 + h^2

= (15 - 5)^2 + 242

= 100 + 576

l = 676 = 26 cm^2

Area of metal sheet used in making bucket

= CSA of bucket + area of smaller circular base

$\bf\huge = \pi (r_{1} + r_{2} )l + \pi r^{2}$

$\bf\huge = \pi (r_{1} + r_{2})\: l + r^{2}$

= 3·14{(5 + 15)26 + 52}

= 3·14(520 + 25)

= 3·14 × 545

Area of metal sheet used in making bucket

= 1711·3 cm^2