Question

58. 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

Answer:

for petrol tank in the form of frustum of cone,

lower diameter d = 20 m

lower radius r = 10 m

And upper diameter = D = 50 m

 upper radius R = 25 m

Therefore, volume of petrol tank is

∴ V = 20,428.57

∴ V = 20.43 × 103 m3

But 1 m3 = 1000 litre

∴ V = 20.43 × 103× 1000 = 20.43 × 106 litre

Hence, volume of petrol tank is 20.43 × 103 m3.

Now, cost of petrol is Rs 70/litre

Therefore, total cost of petrol is

= 20.43 × 106 × 70 = 1430 × 106 Rs

Now, slant height of cone is

∴ l = 25

Total surface area of frustum of cone

= 2750 + 1964.3 + 314.3

∴ S = 5028.6 m2

Hence, total surface area of petrol tank is 5028.6 m2.

Answer 2

Cost of petrol to fill the tank = 143 crore rupees.

Surface area of tank = 5028.6 m²

Step-by-step explanation:

h = 20m , r = 10m , R = 25m

Volume of a conical frustum: V = (1/3) * π * h * (R² + r² + (R*r))

= 1/3 * 22/7 * 20 *(10² +25² + (10*25))

= 1/3 * 22/ 7 * 20 * (100 + 625 + 250)

= 1/3* 22/ 7 * 20 * 975

=  20,428.57 m³

1m³ = 1000 litres.

Volume of tank in litres = 20,428.57 * 1000 =  20.43 × 10^6 litres

Cost of one litre of petrol = 70

Cost of filling the tank =  20.43 × 10^6  * 70 = 1,43,00,00,000 = 143 crores

Slant height of the frustum = l = root of [(h² + (R -r)²]

= root of [20² + (25-10)²]

= root of (400 + 15²)

= root of (400 + 225)

= root of 625

= 25 m

TSA of the frustum = π l (R+r) + πR² + πr²

= (π * 25 * 35) + (π * 25 * 25) + (π * 10 * 10)

= 2750 + 1964.3 + 314.3

= 5028.6 m²