Question

A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank.​

Answer 1

hey mate

here is ur answer

refer to the attachment

Answer 2

The cost of petrol = 2143.62 Rs.

Total surface area of the tank = 5026.54 cm²

Given:

A petrol tank is in the form of a frustum of a cone of height 20 cm with diameters of its lower and upper ends as 20 cm and 50 cm respectively.

Cost of petrol per liter is 70 Rs.

To find:

The cost of petrol which can fill the tank completely.

The surface area of the tank.​

Formula used:

The Volume of Frustum of Cone = $\frac{1}{3}$× π × h ×  $\frac{R^{3} - r^{3} }{r}$

The total surface area of the frustum of the cone = π ×L× (R+r) +πR² +πr²

           Where R = radius of Lower end

                       r = radius of upper end

                      L = slant height = $\sqrt{h^{2}\ + (R-r)^2 }$

Explanation:

Total petrol filled in tank = Volume of the tank

Radius of Lower end = R =  $\frac{50}{2}$ = 25cm.

Radius of upper end = r = $\frac{20}{2}$ = 10cm.

    Height = h = 20cm.

Volume of Frustum of Cone = $\frac{1}{3}$× π × h ×  $\frac{R^{3} - r^{3} }{r}$

                                              = $\frac{1}{3}$× π × 20 ×  $\frac{25^{3} - 10^{3} }{10}$

                                              = 20.94 × 1462.5

                                              = 30624.75 cm³

1 liter = 1000 cm ³

So

30624.75 cm³ = 30.624 liter

Cost of petrol per liter is 70 Rs.

Cost of petrol for 30.624 liter = 70 × 30.624 = 2143.62 Rs.

Slant height of Frustum of Cone =  $\sqrt{h^{2}\ + (R-r)^2 }$

                                                      =  $\sqrt{20^{2}\ + (25-10)^2 }$  

                                                      = 25 cm.

Total surface area of the tank.​ =  π ×L× (R+r) +πR² +πr²

                                                  = π ×L× (R+r) +πR² +πr²

                                                  = π ×25× (25+10) +π×25² +π ×10²

                                                 = 5026.54 cm²

The cost of petrol = 2143.62 Rs.

Total surface area of the tank = 5026.54 cm²

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