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 `= 1/3pi"h"("R"^2+r^2+Rr)`

`= 1/3 xx 22/7xx24xx(20^2 + 8^2 +20xx8)`

`= 176/7xx(400+64+160)`

`=176/7xx624`

`=109824/7 "cm"^3`

`= 109824/7  "L"`        (As, 1000 cm³ = 1 L)

So, the cost of the millk in the  container `= 109.824/7 xx 21`= 329.4712

≈ ₹ 329.47