M L Aggarwal Solutions for Chapter: Applications of Derivatives, Exercise 1: EXERCISE 7.1

If the radius of a circle is increasing at the rate of $0.7 \mathrm{cm}/\sec$, at what rate is its circumference increasing?

If the radius of a circle is increasing at the rate of $3 \mathrm{cm}/\sec$, at what rate is its area increasing when its radius is $10 \mathrm{cm}$?

If the sides of a square are decreasing at the rate of $1.5 \mathrm{cm}/\sec$, at what rate is its perimeter decreasing?

If an edge of a variable cube is increasing at the rate of  $3 \mathrm{cm}/\sec$ at what rate is its volume increasing when its edge is $10 \mathrm{cm}$?

A cylindrical tank of radius $10 \mathrm{m}$ is being filled with wheat at the rate of $314$ $\mathrm{cubic} \mathrm{metre} \mathrm{per} \mathrm{hour}$. Find the rate at which the depth of the wheat is increasing, take $\mathrm{\pi }=3.14$.

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R\left(x\right) = 3x^2+36x+5$. Find the marginal revenue when $x = 5$.

The length $x$ of a rectangle is decreasing at the rate of $5 \mathrm{cm}/\min$ and the width $y$ is increasing at the rate $4 \mathrm{cm}/\min$ when $x = 8 \mathrm{cm}$, $y = 6 \mathrm{cm}$, find the rate of change of the area of the rectangle.

Water is dripping out at the steady rate of $1 cu cm/sec$ through a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel as $4 cm$, find the rate of decrease of slant height where the semi vertical angle of the cone is $\frac{\mathrm{\pi }}{6}$.