Question

A container open at the top,is in the form of frustum of a cone of height 24cm with radii of its lower and circular ends as 8 cm and 20cm.find the cost of milk which can completely fill the container at the rate of Rs. 21 per litre.

Answer 1

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Answer 2

Answer:

Cost of the milk fill in the frustum is Rs 329.2.

Step-by-step explanation:

Formula

$Volume\ of\ a\ frustum = \frac{\pi h}{3}(R^{2}+Rr +r^{2})$

Where h is the height ,  R and r is the radius of the two bases of the frustum .

As given

A container open at the top,is in the form of frustum of a cone of height 24cm with radii of its lower and circular ends as 8 cm and 20cm.

R = 20 cm

r = 8 cm

h = 24 cm

$\pi = 3.14$

Put all the values in the formula

$Volume\ of\ a\ frustum = \frac{3.14\times 24}{3}(20^{2}+20\times 8+8^{2})$

20² = 400

8² = 64

$Volume\ of\ a\ frustum =3.14\times 8\times (400+160+64)$

$Volume\ of\ a\ frustum =3.14\times 8\times 624$

$Volume\ of\ a\ frustum =15674.88\ cm^{3}$

Thus the volume of the frustum is 15674.88 cm³ .

As

1 litre = 1000 cm³

$1\ cm^{3} = \frac{1}{1000}\ litre$

Now convert 15674.88 cm³ into litres .

$15674.88\ cm^{3} = \frac{15674.88}{1000}\ litre$

                                   = 15.67488 litre

As given

The rate of the milk is  Rs. 21 per litre.

Thus

Cost of the milk = Volume of the frustum × Cost of milk per litre .

                           =   15.67488 × 21

                           = Rs 329.2 (Approx)

Therefore the cost of the milk fill in the frustum is Rs 329.2 .