A container, open from the top and made up of a metal sheet is the form of frustum of a cone of height 30 cm with radii 30 cm and 10 cm. Find the cost of the milk which can completely fill container at the rate of Rs.30 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.50 per 100 cm². (????= 3.14)
Answers
Answer:
Capacity of frustum of cone in litres = 40.84 litres
Cost of milk @ 30 per litre ≈ 1225 Rupees
Cost of sheet required to make that container = 3298.67 ≈ 3299 Rupees
Solution:
Volume of frustum of cone = 1/3 π × h (r² + rR + R²)
r = 10 cm
R = 30 cm
h = 30 cm
Volume of frustum of cone = 1/3 π × 30 ( 10² + 30(10) + 30²)
Volume of frustum of cone = 1/3 π × 30 ( 100+300+900)
= 10 π (1300)
= 13000 π
= 40,840.70 cm³
As we know that 1 litre = 1000 cm³
Capacity of frustum of cone in litres = 40,480.70/1000 = 40.84 litres
Cost of milk @ 30 per litre = 40.84 × 30 = 1225.22 ≈ 1225 Rupees
Now, to find how much metal sheet is required :
Total Surface area of frustum of cone - area of top
= π( r + R)h + πr² + πR² - πr²
= π( r + R)h + πR²
= π( rh + Rh + R²)
= π ( 10 × 30 + 30 × 30 + 30²)
= π (300+900+900) = π(2100)
Total metal sheet require = 6597.34 cm²
Given that Cost is 50 rs per 100 cm²
Total cost = 6597.43 × 50/100
= 3298.67 ≈ 3299 Rupees
Hope it helps you.
