Question

The side of a cube is increasing at the rate of 5cm⁻¹. Find the rate of increase of the volume when the length of a side is 3cm.

A) 45 cm³/s
B) 90 cm³/s
C) 135 cm³/s
D) 180 cm³/s

Answer 1

The rate of increase of the volume when the length of a side is 3cm is 45 cm³/s.

Step-by-step explanation:

To find the rate of increase of the volume, we need to differentiate the volume formula of a cube with respect to time. The volume of a cube is given by V = s³, where s is the length of a side. Differentiating both sides of the equation with respect to time, we get dV/dt = 3s²(ds/dt). Given that ds/dt = 5 cm⁻¹ and s = 3 cm, we can substitute these values into the equation to find the rate of increase of the volume.

dV/dt = 3(3)²(5) = 45 cm³/s

Therefore, the rate of increase of the volume when the length of a side is 3cm is 45 cm³/s. The correct answer is A) 45 cm³/s.