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

1. Identify the given values

The dimensions of each frustum-shaped container and the camp’s requirements are:

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

2. Calculate the container volume

The formula for the volume (V) of a frustum of a cone is:

`V = 1/3 πh (R^2 + r^2 + R xx r)`

Substituting the given values (taking `π = 22/7`):

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

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

`V = 220/7 xx 2800`

V = 220 × 400

V = 88000 cm³

3. Convert volume to litres

Since 1000 cm³ = 1 litre:

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

4. Find the required containers

To find the number of containers required daily to hold 8800 litres of milk:

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

Number of containers = `8800/88` = 100 containers

5. Determine the total cost

To calculate the total daily expense of the milk at the rate of ₹ 35 per litre:

Daily cost = 8800 litres × 35/litre

Daily cost = 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.