A container, open 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 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs 10 per 100cm2. [Take a = 3.14]pls help me to solve this ​

AshjexBG AshjexBG Best Answer 1 year ago

Radius r 1 of upper end of the container=20cmRadius r 2 of lower end of the container=8cmHeight h of the container=16cmSlant HEIGHT l of the frustrum= (r 1 −r 2 ) 2 +h 2 = (20−8) 2 +16 2 = 144+256 =20cmCapacity of container=Volume of the frustrum= 31 πh(r 12 +r 22 +r 1 r 2 )= 31 ×3.14×16(20 2 +8 2 +20×8)= 31 ×3.14×16(400+64+160)= 31 ×3.14×16×624=10449.92 cubic.cm=10.45litresCost of 1 litre of milk=Rs20Cost of 10.45 litre of milk=Rs20×10.45=Rs209Area of METAL sheet used to make the container=π(r 1 +r 2 )l+πr 22 =π(20+8)20+π8 2 =560π+64π=624πsq.cmCost of 100sq.cm metal sheet= Rs.8Cost of 624πsq.cm metal sheet = 100624×3.14×8 =156.75∴ the COST of the milk which can completely fill the container is Rs209and the cost of metal sheet used to make the container is Rs.156.75

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