Question

A donor agency ensures milk is supplied in containers, which are in the form of a frustum of cone to be distributed to flood victims in a camp. The height of each frustum is 30 cm and the radii of lower and upper circular ends are 20 cm and 40 cm respectively. If this milk is available at the rate of ₹ 35 per litre and 8800 litres of milk is needed daily for a camp.

1. Find how many milk containers are needed daily for the camp. 
2. What daily cost will put on the donor agency?

Answer 1

Given:

Lower radius (r) = 20 cm

Upper radius (R) = 40 cm

Height (h) = 30 cm

Total daily milk requirement = 8800 litres

Cost of milk = 35 per litre

Value of π = `22/7`

a. Find the number of milk containers required daily:

First, find the volume of one frustum-shaped container:

`V = 1/3 πh (R^2 + r^2 + R xx r)`

= `1/3 xx 22/7 xx 30 xx (40^2 + 20^2 + 40 xx 20)`

= `10 xx 22/7 xx (1600 + 400 + 800)`

= `220/7 xx 2800`

= 220 × 400

= 88000 cm³

Convert the volume from cm³ to litres (Since 1000 cm³ = 1 litre):

Capacity of one container = `88000/1000` = 88 litres

Now, calculate the total number of containers needed:

Number of containers = `"Total daily milk needed"/"Capacity of one container"`

= `8800/88`

= 100 containers

b. Find the total daily financial expense incurred by the donor agency:

Total daily cost = Total daily milk needed × Cost per litre

= 8800 × 35

= 3,08,000

The donor agency requires 100 milk containers daily, putting a total financial expense of ₹ 3,08,000 per day on the agency.