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Ctrlv open at the topand made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm2. Useπ=3.14
Asked by Jainkumkum2335 | 22 Feb, 2019, 10:14: AM
answered-by-expert Expert Answer
Figure shows the crosssection of bucket which is in frustum shape along with the cone from which the frustum is made.
 
since ΔGEC and ΔGFB are similar, we have begin mathsize 12px style fraction numerator h over denominator h plus 24 end fraction space equals space 5 over 15 end style  ; we get h = 12 cm from this relation
Surface area of bucket to calculate the required metal sheet = π×R×L - π×r×l - π×r2 = π×(R×L - r×l -r2 ).....(1)
where L and l  are respective slanting height of bigger and smaller cone. R = 15 cm and r = 5 cm
 
hence from (1), we have,  begin mathsize 12px style straight pi open parentheses 15 square root of 15 squared plus 36 squared space end root space minus 5 square root of 5 squared plus 12 squared end root space plus space 25 space close parentheses space equals space straight pi cross times 545 space cm squared end style
cost of metal sheet = π×545×(10/100) = Rs. 171
Answered by Thiyagarajan K | 22 Feb, 2019, 11:22: AM

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