Lengths of Curves. • =S/{1 + (dz¥)3}dx. Parabola, s = √ ax + x2 + a log √x + √α+ x; = S2xyds= S 2ny de dy = S 2xy ds dx. dx Sphere, s = 4πr2; Cylinder, s = 2πr (x2—X1); Frustum of cone s = tan a sec a Cone, sπ cosec ar2. Paraboloid, s = 8TM√a{(x+a)3 — al}. 3 4 Oblate spheroid, v= Ta2b; Solid generated by revolu 3 (3π2 8) tion of cycloid about its axis, v = ña3 2 22 CIVIL SERVICE PAPERS. I. 1. Write in figures one million four hundred and eighty-seven thousand six hundred and twenty-three; and express in words 70600804016003. 2. From £4768954 13s. 74d. take £2989767 18s. 11ąd. 3. (1) Multiply £2487 14s. 21d. by 3076: (2) divide £7652194 Os. 9d. by 3076. 4. (1) Add,,, (2) divide of by of: 7: 8 7 (3) Multiply 3321 by 441: (4) divide 2.5 by 32. 5. Calculate the duty at £15 per cent. on £963 15s. 6. What is the income of a person who pays £22 7s. 5d. for income-tax at the rate of 7d. in the pound? 7. Find the value of 136 at £1 7s. 2d. 8. What is the expense of digging a ditch of which the solid content is 5755 cub. yds. at 15s. 72d. per yard. 9. At what rate will the interest on £4127 10s. amount to £92 178. 4 d. in a year? 10. Find the compound interest on £364 for 3 years at 31 per cent. 11. Assuming that 32 bricks will make 9 sq. ft. of pavement, how many will be required to pave a yard 63 ft. long by 36 ft. wide? 12. How much time, in the course of 33 yrs., will a person, who rises at 5 o'clock in the morning, gain over another, who rises at 8 o'clock ? supposing both to go to bed at 10 P.M. and computing 365 days to the year. II. 1. Express in figures (1) Nine millions ten thousand and nineteen; (2) Five thousand and six million eight thousand and ninety-four. |