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 1.2g, then find the cost of oil in the container if it costs Rs 40 per kg.

Question

Philoid · Accepted Answer

Given: height of container/frustum = h = 14 cm

Diameter of top of container = 35 cm

Diameter of bottom of container = 30 cm

∴ Radius of top = R = 35/2 = 17.5 cm

∴ Radius of bottom = r = 30/2 = 15 cm

1 cm³ of oil = 1.2g of oil

Cost of 1 kg oil = 40 Rs

Volume of oil in container = volume of container which is in form of frustum

= (22/3) × 2 × (306.25 + 225 + 262.5) cm³

= (22/3) × 2 × 793.75 cm³

= 34925/3 cm³

= 11641.667 cm³

∴ Volume of oil in container = 11641.667 cm³

∴ 11641.667 cm³ of oil = 11641.667 × 1.2 g

= 13970.0004 g

We know 1000 g = 1 kg

∴ 13970.0004 g = 13970.0004/1000 kg

= 13.970 kg

∴ Cost of 13.970 kg oil = 13.970 × cost of 1 kg oil Rs

= 13.970 × 40 Rs

= 558.8 Rs

∴ Cost of oil in container = 558.8 Rs

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 cm3 of oil has mass 1.2g, then find the cost of oil in the container if it costs Rs 40 per kg.

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 cm³ of oil has mass 1.2g, then find the cost of oil in the container if it costs Rs 40 per kg.