A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. If each cm 3 of oil has mass 1.2 g, then find the cost of oil in the container if it costs 40 per kg.

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This question was asked in 2009 cbse board exam.

Problem from RS Aggarwal book, problem number 10, page number 823, exercise 17C, chapter volume and surface area of solid.
Chapter Mensuration

Solution

given data

Diameter of top of container = 35 cm

Radius of top = R = 35/2 = 17.5 cm

Diameter of bottom of container = 30 cm

Radius of bottom = r = 30/2 = 15 cm

1 cm

^{3}of oil = 1.2g of oilCost of 1 kg oil = Rs. 40

Height of frustum = h = 14 cm

Volume of frustum of cone = [1/3] π h(R

^{2}+ r^{2}+ Rr)=[ 1/3] * [22/7] * 14(17.5

^{2}+ 15^{2}+ [17.5 * 15])= [22/3] * 2 * 793.75

= 34925/3

= 11641.667

Volume of oil in container = 11641.667 cm

^{3}11641.667 × 1.2 g = 13970.0004 g or 13.970 kg (1000 g = 1 kg)

Cost of 13.970 kg oil = Rs. 20 x 13.970

Cost of 13.970 kg oil = Rs. 558.80

∴ Cost of 13.970 kg oil Rs. 558.80