Question

a container opens at the top and made up of metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16cm and 40 cm respectively find the cost of metal sheet used to make the container if it costs rs. 10per 100cm^2

Answer 1

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Hey Mate !!

Here's your answer !!

The area of metal sheet covered is calculated as:

CSA of Frustum + Base of the Frustum with small radius.

CSA of Frustum = pi * ( R + r ) * l

Where R is the bigger radius and r is the smaller radius ( of the base )

L = √ ( h² + ( R - r )² )

L = √ (16² + ( 20 - 8 )² )

L = √ ( 256 +12² )

= √ 256 +144

= √400

= 20 cm

Therefore CSA of frustum = 22 / 7 × ( 20 + 8 ) × 20

= 22 / 7 × 28 × 20

= 22 × 4 × 20

= 88 × 20

= 1760 cm²

Area of base = pi × r²

= 22 / 7 × 8 

= 176 / 7

= 25.14 cm²

So area of metal sheet = 1760 + 25.14 = 1785.14 cm²

Given that Rs 10 per 100 cm²

So 1785.14 * 10 / 100

= 1785.14 / 10

= Rs 178.514 which is approximately Rs 178.5.

Hope this helps !!

Cheers !!
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# Kalpesh :)