This is one of the important question from the cbse board exam point of view because in 2014 cbse board exam this question was asked. Question number 4 from RS Aggarwal book page number 823, exercise 17C, chapter volume and surface area of solid.
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A container, open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm, respectively. Find the cost of milk which can completely fill the container at the rate of 21 per liter.
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given data,
Height, h=24 cm,
Upper radius, R=20 cm
Lower radius, r=8 cm
Volume of the container = [1/3] π h [R²+r²+rR]
=[1/3]×[22/7]×24×[20²+8²+[20×8]]
=1767×400+64+160
=1767×624
=109.8247 L
1000 cm³=1 L
∴ the cost of the milk in the container=109.8247×21
=329.472
∴ the cost of milk which can completely fill the container at the rate of Rs. 21 per litre is 329.472