Question

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

Answer 1

$\huge{\boxed{\mathbb{\red{ANSWER}}}}$

The cost of the milk fill in the frustum is Rs 329.2

$\huge{\boxed{\mathbb{\red{EXPLANATION}}}}$

Formula

volume of frustum = πh/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

π = 3.14

Put all the values in the formula

Volume of frustum =

$\frac{3.14 \times 24}{3} \times ( {20}^{2} + 20 \times 1 \times 8 + {1 \times 8}^{2} )$

${20}^{2} = 400 \\ {8}^{2} = 64$

$volume \: of \: frustum = 3.14 \times 8 \times (400 + 160 + 64) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 8 \times 624 \\ volume \: of \: frustum \: = 15674.88 \: {cm}^{2}$

Thus the volume of the frustum is 15674.88 cm³ .

As

1 litre = 1000 cm³

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

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 .

Answer 2

Step-by-step explanation:

The cost of the milk fill in the frustum is Rs 329.2

\huge{\boxed{\mathbb{\red{EXPLANATION}}}}

EXPLANATION

Formula

volume of frustum = πh/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

π = 3.14

Put all the values in the formula

Volume of frustum =

\frac{3.14 \times 24}{3} \times ( {20}^{2} + 20 \times 1 \times 8 + {1 \times 8}^{2} )

3

3.14×24

×(20

2

+20×1×8+1×8

2

)

\begin{lgathered}{20}^{2} = 400 \\ {8}^{2} = 64\end{lgathered}

20

2

=400

8

2

=64

\begin{lgathered}volume \: of \: frustum = 3.14 \times 8 \times (400 + 160 + 64) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 8 \times 624 \\ volume \: of \: frustum \: = 15674.88 \: {cm}^{2}\end{lgathered}

volumeoffrustum=3.14×8×(400+160+64)

=3.14×8×624

volumeoffrustum=15674.88cm

2

Thus the volume of the frustum is 15674.88 cm³ .

As

1 litre = 1000 cm³

{1cm}^{3} = \frac{1}{1000} \: litre1cm

3

=

1000

1

litre

Now convert 15674.88 cm³ into litres .

15674.88 \: {cm}^{3} = \frac{15674.88}{1000} \: litre15674.88cm

3

=

1000

15674.88

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 .