A bucket, is in the form of frustum of a cone whose height is 42 cm and the radii of its circular ends are 30 cm and 10 cm. Find the amount of milk (in liters) which this bucket can hold. If the milkman sells the milk at the rate of Rs. 40 per litre, what amount he will get from the sale?

If the milkman sells half the milk at less rate to the economically weaker section of society, what value he exhibits by doing this?

ABDC represents the frustum of the cone

Given:

Height GF = 42 cm.

Radius GB = 30 cm.

Radius FD = 10 cm.

In ΔABE & ΔCDE

AEB = CED (Common angle)

EDC = EBA (Corresponding angle)

So ΔABE & ΔCDE are similar by A.A. axiom of similarity

Since they are similar we can write

⇒

⇒

⇒ 3EF = EF + 42

⇒ 2EF = 42

⇒ EF = 21 cm

Height GE = 63 cm

Volume of Cone CDE =

Volume of Cone CDE = 2200 cm³

Volume of Cone ABE =

Volume of Cone ABE = 59400 cm³

Volume of Frustum of cone ABDC = Volume of Cone ABE- Volume of Cone CDE

Volume of Frustum of cone ABDC = 57200 cm³ = 57.2 liters

Rate of Milk per Liters = Rs. 40

Answer: Amount he will get from milk = Rs. 2288