fractional 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..

If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all ..

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..

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..

Calculate the trapezoidal approximation T n to the integral ∫ 0 π/2 cos xdx . Use n = 3 subintervals and round the answer to two decimal places. => 0.97 or 0.98 or 0.82 or 10.75..

Dividing the interval [0, π 2 ] into 4 equal subintervals, find the approximate value of ∫ 0 π/2 (cos x + sin x ) dx . => 1.9735 or 3.554 or 3.947 or 0 or 2..

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

(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) R..

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 ..