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

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Surface area of frustum is 2750 m² and cost of petrol that completely fills the tank is Rs.1430000000.

Surface area of frustum is 275 m² and cost of petrol that completely fills the tank is Rs.1430.

Surface area of frustum is 2750 m² and cost of petrol that completely fills the tank is Rs.143.

Surface area of frustum is 2750 m² and cost of petrol that completely fills the tank is Rs.130000000.

answer is A.

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Detailed Solution

Given that,
Height of Frustum of a Cone (h) = 20 m,
Upper Diameter (D) = 50 m,
Lower Diameter (d) = 20 m.
Also given, cost of 1 litre of petrol = Rs. 70.
Now let us find the upper radius and lower radius of a frustum of a Cone.
Radius = diameter/2
Upper radius, R =

\frac{D}{2}

R =

\frac{50}{2}

R = 25 m
Lower radius, r =

\frac{d}{2}

r =

\frac{20}{2}

r = 10 m

We know that,
Volume of frustum

= 13 π h R 2 + R r + r 2

.
The volume of the tank = Volume of the frustum,
V

= 13 π h R 2 + R r + r 2

V = 13 × π × 20 × 252 + 102 + 25 × 10 V = 13 × π × 20 × (625 + 100 + 250) V = 13 × π × 20 × (975) V = π × 20 × 325 m 3

Therefore, Cost of petrol = Volume of a frustum of a cone × Rate of 1 l of petrol.

cost of petrol = (π × 20 × 325) m 3 × 70 cost of petrol = 227 × 20 × 325 × 1000 × 70 1 ∵ 1 m 3 = 1000 I cost of petrol = (22 × 20 × 325 × 1000 × 10) I cost of petrol = Rs .1430000000

We know, Slant height of frustum of a cone

= h 2 + (R − r) 2

,
Curved surface area of frustum of cone = π l × ( R + r ).
The slant height of cone is

l = h 2 + (R − r) 2 = 202 + (25 − 10) 2 = 400 + (15) 2 = 400 + 225 = 625 1 = 25 m

Now, let us find the surface area of the frustrum.

Surface area of frustum = π l × (R + r) Surface area of frustum = 227 × 25 (25 + 10)

Surface area of frustum = 227 × 25 × 35 Surface area of frustum = 22 × 25 × 5

Surface area of frustum

= 2750 m 2

Hence, the surface area of frustum = 2750 m²
Therefore, the cost of petrol which can fill the tank completely at the rate of Rs. 70 per liter is Rs.1430000000 and the surface area of the tank is 2750 m².
The correct option is (1).

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