Question

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 ₹ 30 per litre, which the bucket can hold.

Answer 1

We have,

Height of the frustum, h = 24 cm and 

Radius of the open end, `"R" = 42/2 = 21  "cm" and`

Radius of the close end, `"R" = 28/2 = 14  "cm"`

Now,

Volume of the bucket `= 1/3 pi"h"("R"^2+"r"^2 + "Rr")`

`=1/3xx22/7xx24xx(21^2+14^2+21xx14)`

`=176/7xx(441+196+294)`

`=176/7xx931`

= 23408 cm³ 

= 23.408 L     (As, 1000 cm³ = 1 L)

∴ The cost of the milk which the bucket can hold is ₹ 702.24