rational approximations of pi

Earth is not a perfect sphere, but nearly so, with the approximate surface area 510926783 km 2 . Find the earth's diameter approximately. (Use π = 3.14) => 7198 km or 12756 km or 6378 km or 3189 km..

A metallic solid in the form of a square pyramid of base 16 cm and height 2 cm is melted to make conic pieces of base radius 3 cm and height 3 cm. How many pieces can be made approximately? [Take π = 3.] => 35 or 25 or 28 or 6..

Use f ( x ) = sin x to approximate the value of sin (3.14). [Take π = 3.1415926] => - 1 or 0 or - 0.0015926 or 0.0015926 or 1..

Name the subset(s) of the real numbers to which " π " belongs. => integers, Rational numbers, Real numbers or whole numbers, integers, rational numbers, real numbers or natural numbers, whole numbers, integers, rational numbers, real numbers or irrational ..

Use f ( x ) = Tan - 1 x to approximate the value of Tan - 1 (1.09). [Take π = 3.1415926] => 0.57 or 1.09 or 0.35 or 0.75 or 0.83..

Calculate the trapezoidal approximation T n to the integral ∫ 0 π/3 tan x dx . Use n = 5 subintervals and round the answer to two decimal places. => 0.37 or 0.47 or 0.67 or 0.27..

An athlete was running on a circular track of diameter 160 m. He first started at a point and ran 2 3 distance of the track length, in clockwise direction and ran 1 3 distance of the track length, in anti clockwise direction. Find the total distance he ran. [Approximate the distance to th..

Find the approximate volume generated by rotating about the x - axis the plane region bounded by y = 4 - x 2 and y = 0. => 32 π or 30 π or 34 π or 33 π..

Irrational Numbers - Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. i.e., Irrational numbers cannot be put in the form where and are some examples of irrationals. (i) is also irrational. Its a..

Nature of the roots - Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are rational a..