Question

Water is pouring into a conical vessel of diameter 5.2m and slant height 6.8m (as shown in the adjoining figure), at the rate of 1.8 m per minute. How long will it take to fill the vessel?​

Answer 1

31.6m

Explanation:

First, find area of the vessel [ (πr2h)/3 ]

Radius = 5.2/2= 2.6

Using Pythagorean theorem, find the height of the cone:

`\sqrt{6.8^(2) -5.2^(2) }` = 4.38

Area of vessel =
`( (PI * 2.6 * 2 * 4.38))/(3)` = 56.88
`cm^(3)`

Do cross multiplication using ratios:

1.8 = 1

56.88 =
`x`

`(56.88)/(1.8)`= 31.6