Question

A cylindrical popcorn tub of radius 10 cm is being filled with popcorns at the rate of 314 cm³ per minute. The level of the popcorns in the tub is increasing at the rate of:

Options

• 1 cm/minute

• 0.1 сm/minute

• 1.1 сm/minute

• 0.5 сm/minute

Answer 1

1 cm/minute

Explanation:

Given, radius (r) = 10 cm

`"dV"/"dt"` = 314 cm³/min

`"dh"/"dt"` = ?

We know that

Volume of cylinder

V = πr²h

V = π(10)²h

V = 100πh

⇒ `"dV"/"dt" = 100π "dh"/"dt"`

⇒ `314 = 100π "dh"/"dt"`

⇒ `"dh"/"dt" = 314/(100 xx 3.14)`

⇒ `"dh"/"dt"` = 1 cm/min