Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(a) Textbook Exercise Questions and Answers.

## CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Exercise 8(a)

Question 1.

Find the velocity and acceleration at the end of 2 seconds of the particle moving according to the following rules.

(i) s = 2t^{2} + 3t + 1

Solution:

s = 2t^{2} + 3t + 1

∴ Velocity is 11 units/sec and acceleration is 4 units/sec^{2}.

(ii) s = √t +1

Solution:

s = √t +1

(iii) s = \(\frac{3}{2 t+1}\)

Solution:

(iv) s = t^{3} – 6t^{2} + 15t + 12

Solution:

s = t^{3} – 6t^{2} + 15t + 12

∴ Velocity is 3 units/sec and acceleration is 0.

Question 2.

The sides of an equilateral triangle are increasing at the rate of √3 cm/sec. Find the rate at which the area of the triangle is increasing when the side is 4 cm long.

Solution:

Let x be the lenght of each side of an equilateral triangle.

∴ Area of the triangle is increasing at the rate of 6 cm^{2}/sec

Question 3.

Find the rate at which the volume of a spherical balloon will increase when its radius is 2 metres if the rate of increase of its radius is 0.3 m/min.

Solution:

Let r be the radius of a spherical balloon.

∴ The volume increase at the rate of 4.8π m^{3}/min.

Question 4.

The surface area of a cube is decreasing at the rate of 15 sq. cm/sec. Find the rate at which its edge is decreasing when the length of the edge is 5 cm.

Solution:

Let s be the surface area of a cube.

Let x be the length of each side of the cube.

∴ The edge is decreasing at the rate of 0.25 cm/sec