55. Powers and Roots. Find the powers indicated below : (344.) 192 (347.) 2.5052 (350.) (21) (353.) (* X 11). (345.) 1.92 (348.) 1.0048. (351.) (53) (354.) (+3) (316.) 0.192 (349.) 0.034 (352.) (161) (355.) 1.054. Find the square root 363. Of 0.005648. 358. Of 1633. 361. Of 640900. 364. Of 369056.25. 365. Find the difference between the sum of the square roots of 6075 and 41616 and the square root of their sum. 366. V10,%=? 370. V-14=? 374. V0.4 + 25 =? 367. V934= ? 371. V10025= ? 375. V0.9 X 0.16=? 368. V17}&= ? 372. V27 x (9)2= ? 376. V of f of 1} : ? 369. V424=? 373. Vis of = ? 377. V0.36 -4 X 61 = ? 378. If a square contains 124 square feet, what is the length of one of its sides? 379. On a roof are laid 7200 slates, the number in the length being twice the number in the width. What is the number each way? 380. My orchard contains 7350 trees. The number of trees in width is to the number of trees in length as 2 is to 3. What is the number each way? Find the cube root 381. Of 39304. 384. Of 4104. 387. Of 0.27. 390. 1525 382. Of 103.823. 385. Of 79.507. 388. Of 6.4. 391. 383. Of 0.00043. 386. Of 2.24. 389. Of 0.8. 392. Vi}= ? 393. Maury estimates the annual amount of rainfall in the Mississippi Valley to be 620 cubic miles of water, of which 107 cubic miles is poured into the sea. What would be the depth of a cubical reservoir that would contain the remainder ? 394. It is estimated that in 1871 the world's consumption of petroleum was 6,000,000 barrels. If each barrel contained 50 gallons, what would be the length of a cubical tank large enough to contain it all ? =? 345= ? 8 56. Mensuration. RECTILINEAR FIGURES. 395. Find the area of a rectangle whose base is 7 m and whose height is 5.4 m 396. Miss Gove has a triangular flower-bed whose sides are 10 feet, 15 feet, and 9 feet long respectively. How many square feet are there in the bed ? 397. Of two triangular flower-beds, one having each of two sides 8 feet in length and the third side 12 feet, the other having a right angle enclosed by two sides each 7 feet long, which is the larger, and how much larger? 398. How many yards of lace must be used to trim the edge of a “half-handkerchief,” the length of the diagonal side being 28 inches, and 4 inches being allowed for fulness around each corner ? 399. Wishing to find the distance between two points A and B, on opposite sides of a swamp, I measured two lines A C and B C, from A and B, making a right angle at C, and found them to be 60 feet and 80 feet long respectively. How far was A from B ? 400. How many ars are there in a square field whose diagonal is 100 meters ? 401. Find the area in acres of a rectangular field whose length is 10 chains and breadth 8.49 chains. [See page 306, Art. 19.] 402. If the area of a parallelogram is 500 square yards and its height is 50 feet, what is its base ? 403. Two parallel sides of a quadrilateral field are 45 chains and 36 chains respectively, the distance between them is 25.4 chains. How many acres are there in the field ? 404. The sides of a quadrilateral field are 50 chains, 43.4 chains, 26.8 chains and 43.2 chains respectively; the length of a diagonai cutting off the first two sides is 53 chains. How many acres are there in the field ? CIRCLES. 405. How far must I go to walk from one point in the circumference of a circular pond to the opposite point, if it is 40 feet across ? 406. If it is 36 feet around the casing of a circular window, how far is it across ? 407. How many square yards of turf will be required to cover a circular plat of ground 27 feet across ? 408. If the area of a circular park is 12 acres, how long must a fence be to enclose it? [Ans. in rods.] 409. If the area of a circle is 40 square feet, what is the area of an inscribed square ? 410. If the side of a square inscribed in a circle is 40 chains, what is the area of the circle ? SOLIDS. 411. Find the entire surface of a cube each of whose edges is 2 feet long. 412. Find the entire surface of a rectangular solid whose dimensions are 2 feet, 3 feet, and 4 feet respectively. 413. Find the convex surface of a regular pentagonal column whose height is 10 ft. and the width of each of whose faces is 1 ft. 3 in. 414. Find the convex surface of an octagonal block whose slant height is 6 inches, the length of each side of the upper base being 7 inches and that of the lower base being 9 inches. 415. Find the convex surface of a regular 4-sided pyramid 12 feet high, the length of one side of the base being 10 feet. 416. Find the number of cubic feet in the pyramid named in Example 415. 417. If the pyramid named in Example 415 be cut by a plane parallel with the base and 2 feet from it, how many cubic feet will be contained in the lower part ? 418. How many cubic feet are there in a piece of timber 15 feet long, 16 inches square at one end and 12 inches square at the other ? 419. Find the convex surface of a pipe 2 meters long, the diameter of which is 36 centimeters. 420. Find the convex surface of a cone a meter high, the radius of the base being 3 decimeters. 421. How many square inches in the surface of the largest sphere that can be put into a cubical box whose dimensions on the inside are 14 inches each ? 422. How many cubic feet of air may be contained within a conical tent the diameter of the base being 25 feet and the slant height 20 feet 10 inches ? 423. How many square feet of canvas will cover a conical tent, the diameter of the base being 28 feet and the height 13 feet ? 424. How many cubic inches of water can be contained in a globe whose diameter inside is 15 inches ? a, study; 6, hall; c, sitting-room; d, dining-room ; e, conservatory ; , , , piazza. 425. Above is a plan of some rooms in a house. If you should carpet the study with ingrain carpeting a yard wide, and lay it down so as not to split any breadth nor turn any under, how many yards would you use, nothing being allowed for matching the figures ? 426. How many yards would you use to carpet the study if you should lay the carpeting down lengthwise of the room and should not split any breadth, nothing being allowed for matching figures ? What will be the cost of the carpeting at $ 1.25 per yard ? 427. How many yards of Brussels & yd. wide will it take to carpet the sitting-room, if the breadths are laid lengthwise of the room and one breadth is split into two equal parts, no allowance being made for matching figures ? What will be the cost of the carpeting at $ 2.25 per yard ? 428. If the cost of carpet for carpeting the sitting-room with Brussels carpet be $87.75, what will be saved by carpeting it with ingrain at $1.25 per yard, laying the breadths lengthwise of the room, and splitting no breadth ? 429. How many square feet are there in the floor of the diningroom if the bay window is 2 feet deep and 9 feet wide ? 430. How many square feet are there in the floor of the hall ? NOTE. In solving Examples 430 and 432, no allowance is made for thickness of walls. 431. How many square feet in the floor of the conservatory if it is 8 feet in front, 10 feet at the back, and 3 feet deep ? 432. How many square feet in the floor of the piazza if it is 5 feet wide ? 433. Wishing to carpet the stairs as shown in the plan, I found the height of the second floor from the hall floor to be 10 feet. Allowing half a yard for the landing, etc., what would be the cost of carpeting at $2.127 per yard ? 434. The back stairs are 14 in number and carpeted with tapestry at 873% per yard, 5% off for being damaged. Each stair is 8 inches high, and 8 inches wide, and of a yard is allowed for turnings, etc. What is the cost of the carpeting? 435. In the dining-room is an extension-table 4 feet wide. The ends of the table are semicircular, and besides there are 6 leaves each 15 inches wide. How many square feet are there in the surface of the table and leaves, and what is the greatest number of people that can be seated around it, allowing 2 feet for each person ? 436. When 3 leaves are in, how long must the table-cloth be to . cover the table and hang a quarter of a yard over at each end ? 437. What is the cost of a concrete walk 10 feet wide extending diagonally across a square park containing 1 acre, the concrete costing 8% a square foot ? 438. At $3.50 a yard, what is the cost of a piece of velvet, the length of one side on the selvage being 24 yards, and of the other being 3} yards? 439. At $ 2.60 a yard, what is the cost of a piece of satin 27 inches wide cut off at one end at right angles with the selvage, and at the other end being cut on a bias” (making half a right angle with the selvage), the length of the longer side of the satin being 21 yards ? 440. On a piece of land 10 rods long, 7 rods wide at one end and 5 rods wide at the other, 1 bushel of oats was sown. This was at the rate of how many per acre ? 441. There are 3,000,000 cu. ft. of masonry in the Victoria Bridge at Montreal. If this masonry was put into a pyramidal form whose base was square and whose height equalled that of Bunker Hill Monument (221 feet), what would be the length of one side of the base ? 442. How hectoliters of water may be contained in a reservoir 10 meters deep, 360 meters square at the bottom, and 400 meters square at the top ? many |