Question

A Container, open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular end as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of ₹21 per litre. ​

Answer 1

Given :

• Height of the cone Frustum = 24 cm

• Inner Radius = 8 cm

• Outer Radius = 29 cm

• Cost of milk per litre = ₹ 21

To find :

The cost of milk in the whole container.

Solution :

Since we have to find the cost of milk which can be contained in the whole container, first we have to find the volume of the container.

We know the formula for volume of a Frustum i.e,

$\boxed{\bf{V = \dfrac{1}{3} \pi rh\big(R^{2} + Rr + r^{2}\big)}}$

Where :-

• r = Inner Radius
• h = Height
• R = Outer Radius

Now , using the above formula and substituting the values , we get :

$:\implies \bf{V = \dfrac{1}{3} \pi rh\big(R^{2} + Rr + r^{2}\big)}$

$:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(20^{2} + 20 \times 8 + 8^{2}\big)}$

$:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(400 + 160 + 64\big)}$

$:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(604\big)}$

$:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \times 604}$

$:\implies \bf{V = \dfrac{850432}{7}}$

$:\implies \bf{V = 121490.3\:cm^{3}}$

$\boxed{\therefore \bf{Volume\:(V) = 121490.3\:cm^{3}}}$

Hence, the volume of the Cone Frustum is 121490.3 cm³.

To find the cost of milk :

Since , the cost is given in litre we will changed volume in litre.i.e,

121490.3cm³ = 121.49 litres.

Now , to find the total cost , we have to find the product of the volume and cost of 1 litre of milk. i.e,

==> Rs. (121.49 × 21)

==> Rs. 2551.29

Hence, the total cost is Rs. 2551.49.

Answer 2

Given

• A Container, open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular end as 8 cm and 20 cm respectively.

We Find

• The cost of milk which can completely fill the container at the rate of ₹21 per litre.

We Used

• Formula used :- Volume of Frustum

According to the question

$</p><p></p><p>\begin{gathered}:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(20^{2} + 20 \times 8 + 8^{2}\big)} \\ \\ \\\end{gathered} \\ \\</p><p></p><p> </p><p></p><p>\begin{gathered}:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(400 + 160 + 64\big)} \\ \\ \\\end{gathered} \\ \\</p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \big(604\big)} \\ \\ \\\end{gathered} \\ \\</p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies \bf{V = \dfrac{1}{3} \times \dfrac{22}{7} \times 8 \times 24 \times 604} \\ \\ \\\end{gathered} \\ \\</p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies \bf{V = \dfrac{850432}{7}} \\ \\ \\\end{gathered} \\ \\</p><p></p><p> </p><p> </p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies \bf{V = 121490.3\:cm^{3}} \\ \\ \\\end{gathered} </p><p>$

Let's Find the cost of milk

Cost of milk = volume of container / ₹21 per litre

Cost of milk = 121490.3 / 21

Cost of milk = 5785.25

Hence cost of Milk is ₹ 5785.25