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..

Find the approximate value of ∫ 0 π sin x dx , by using 4 rectangles of equal width. => 0.785 or 2.414 or 2.785 or 1.414 or 1.895..

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 sin xdx . Use n = 4 subintervals and round the answer to two decimal places. => 1.90 or 1.88 or 0.95 or 2.31..

If an error of 0.08 cm is made while measuring the radius 10 cm of a sphere, then approximate the propagated error in its volume. => 1333.33 π cm 3 or 10.67 π cm 3 or 320 π cm 3 or 6.4 π cm 3 or 32 π cm 3..

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..

From the above examples on approximation, we observe that the approximated value may be more or less than the original number. The difference between these two values is called the absolute error. Absolute Error = Original number - Approximated number The ratio of the ..

(i) Radioactive dating This gives us an approximate age of the rock or material containing the radioactive atoms. For e.g., A measurement of a fraction of uranium atom which have decayed into lead (by knowing the half life of uranium) tells us how old the rock is. (ii) Radiation f..

Introduction - We use specific number of digits to denote an exact value of a number for required accuracy. The digits used for such a purpose are called significant figures. Suppose a measurement is recorded as 0.6204 cm. It means that the measurement was made correct to the nearest 0.0001 cm. The..