A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs 30 per litre, which the bucket can hold.
Upper end radius of frustum = d/2= 28/2 = 14 cm
Lower end radius of frustum = D/2 = 42/2 =21 cm
Height of the frustum = 24 cm
And we know,
The amount of milk that bucket can hold = Volume of the bucket
And, Volume of bucket = Volume of Frustum
∴ Amount of milk that bucket can hold = Volume of frustum
⇒Volume of frustum
Where R = Radius of larger or lower end and r = Radius of smaller or upper end and h = height of frustum π = 22/7
⇒Volume of frustum
= 22 × 8 × 133
∴ Volume of frustum = 23408 cm3
Also we know that 1 litre = 1000 cm3
⇒ Volume of frustum in litre = 23408/1000= 23.408 litre
⇒ Amount of milk that the bucket hold = 23.408 litre
⇒ The cost of milk = Rate of milk × amount of milk bucket holds
⇒ The cost of milk = 30 × 23.408
∴ = Rs. 702.24
The cost of milk is Rs.702.24