Question

An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is ______ cm³/s.

Options

• 600

• 700

• 800

• 900

Answer 1

An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is 900 cm³/s.

Explanation:

Volume of cube,

V = xyz

Put x = y = z

V = x³

Differentiate above equation

w.r.t time, we get

`(dV)/(dt) = 3x^2 xx (dx)/(dt)`

Given, `(dx)/(dt) = (3cm)/sec`

x = 10 cm

`(dV)/(dt) = 3 xx 100  cm^2 xx (3cm)/sec`

`(dV)/(dt)` = 900 cm³/s