Question

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

Answer 1

We have,

Height, h = 14 cm

Rdius of upper end, `"R"=35/2 = 17.5  "cm" and`

Radius of lower end, `r = 30/2 = 15  "cm"` 

Now,

Volume of the container `= 1/3pi"h"("R"^2+"r"^2+"Rr")`

`= 1/3xx22/7xx14xx(17.5^2+15^2+17.5xx15)`

`= 44/3 xx (306.25 + 225 + 262.5)`

`=44/3xx793.75`

`=34925/3  "cm"^3`

So, the mass of the oil that is completely filled in the container`= 34925/3 xx 1.2`

= 13970 Kg

= 13.97 Kg

∴ The cost of the oil in the container = 40 ×1.2

= 13970 Kg

= 13.97

∴ The cost of the oil in the container = 40 × 13.97 = ₹ 558.80