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 ends 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

We have,

Height, h = 24 cm,

Upper radius, R = 20 cm ad 

Lower radius, R =  8 cm

Now,

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 ends 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.

Volume of the the container ${\displaystyle =\frac{1}{3}\pi \text{h}({\text{R}}^2+r^2+Rr)}$

${\displaystyle =\frac{1}{3}\times \frac{22}{7}\times 24\times ({20}^2+8^2+20\times 8)}$

${\displaystyle =\frac{176}{7}\times (400+64+160)}$

${\displaystyle =\frac{176}{7}\times 624}$

${\displaystyle =\frac{109824}{7}{\text{cm}}^3}$

${\displaystyle =\frac{109824}{7} \text{L}}$        (As, 1000 Cm³ = 1 L)

So, the cost of the millk in the  container ${\displaystyle =\frac{109.824}{7}\times 21}$= 329.4712

≈ ₹ 329.47