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.

OR

Water is flowing at the rate of 15km/hour through a pipe of diameter 14cm into a cuboidal pond which is 50m long and 44m wide. In what time will the level of water in the pond rise by 21cm?

(i) 1430 × 10⁶ Rs (ii) 5028.6 m²

Given –

Height of frustum of cone = h = 20 m

Lower diameter = d = 20 m

Upper diameter D = 50 m

Cost of petrol = Rs. 70/litre

To find – total cost of petrol & surface area of tank

Formulae –

1. Volume of frustum of tank

2. Slant height of frustum of cone

3. Total surface area of frustum of cone

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.

OR

2 hours

Given –

Velocity of water through pipe v = 15 km/hr = 15000 m/hr

Diameter of pipe = d = 14 cm = 0.14 m

Length of pond l = 50 m

Width of pond b = 44 m

Height of water in pond h = 21 cm = 0.21 m

Formulae –

1. Volume of water flowing through pipe = area of pipe × time

2. Volume of cuboid = lbh

Answer –

Let, level of water in pond rises by 21 cm in x hours.

Therefore, volume of water flowed through pipe in x hours is

V = area of pipe × velocity of water × time

= πr² × v × x

∴ V = 231x m³

Now, volume of water in pond upto height 21 cm is

V’ = lbh = 50 × 44 × 0.21 = 462 m³

As volume of water flowed through pipe = volume of water in pond

∴ V = V’

∴ 231x = 462

∴ x = 2

Therefore, it will take 2 hours to increase water level of pond by 21 cm.