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A man donates 10 aluminum buckets to an orphanage. A bucket made of aluminum is of height 20 cm and has its upper

and lowest ends of radius 36 cm and 21 cm respectively. Find the cost of preparing 10 buckets if the cost of aluminum sheet is    

 42 per 100 cm2. Write your comments on the act of the man.

 

 
 
 
 
 

Answers (1)

Bucket in the shape of frustum 

Height = h = 20 cm 

Radius = R = 36 cm 

 radius = r = 21 cm 

Area covered with aluminum  sheet for 10 buckets = CSA of a frustum of cone + area of the bottom 

= \pi l ( R + r ) + \pi r^ 2 \times 10 \\\\ l = \sqrt { h^2 + ( R-r )^2} \\\\ l = \sqrt {20 ^ 2 + ( 15 )^2} \\\\ l = \sqrt { 400 + 225 } \\\\ l = \sqrt { 625 } = 25

= \pi l ( R + r )+ \pi r ^ 2 \times 10 \\\\ = \pi [ l ( R + r )+ r ^ 2] \times 10 \\\\ \frac{22}7{} [ 25 ( 36 + 21 )+ ( 21)^2] \times 10 \\\\ \frac{22}{7} \times 1866 \times 10 \\\\ = 3.14 \times 1866 \times 10 = 58622.1 c m^2 \\\\

therefore the TSA of 10 buckets are = = 58622.1 c m^2 \\\\

cost of aluminum  sheet for 58622.1 c m^2 \\\\  is 58622.1 \times 42/100 = 24621 \\\\

The total cost of the aluminium sheet is rupees 24621

Posted by

Safeer PP

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