List of top Mathematics Questions on Rate of Change of Quantities asked in KEAM

The surface area of a cube is increasing at the constant rate of $0.5 \text{ cm}^2/\text{s}$. Then the rate at which the volume of the cube is increasing (in $\text{cm}^3/\text{s}$), when its surface area has reached $12 \text{ cm}^2$, is
A ladder AB, of length 13m, has one end A on a levelled horizontal ground and the other end B resting against a vertical wall. If the end A begins to slip away from the wall with constant speed 0.25 m/s, and the end B slips down the wall, then the speed of the end B, when B has reached a height of 5m above the ground, is
If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)
When a metallic sphere is heated, maximum percentage change will be observed in its
The surface area of a solid hemisphere is increasing at the rate of \( 8 \, \text{cm}^2/\text{sec} \) (retaining its shape). Then the rate of change of its volume (in \( \text{cm}^3/\text{sec} \)), when the radius is \( 5 \,\text{cm} \), is
Two sides of a triangle are $8$ m and $5$ m in length. The angle between them is increasing at the rate $0.08$ rad/sec. When the angle between the sides is $\frac{\pi}{3}$, the rate at which the area of the triangle is increasing is:
A spherical balloon is being inflated such that its radius increases at a constant rate of \( 2 \,\text{cm/sec} \). The rate at which the volume is increasing when the radius is \( 5 \,\text{cm} \) is
If a circular plate is heated uniformly, its area expands $3c$ times as fast as its radius, then the value of $c$ when the radius is $6$ units, is
The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm the rate of decreasing of its height is:
The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm the rate of decreasing of its height is:
The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm the rate of decreasing of its height is: