177. What is its area?

178. The circumference of a circle is 45.86736 ft. What is its diameter?

179. What is the area of a circle 14' 6" in diameter?

180. How many circles with an area of 2.1 sq. ft. will be contained in a circle with a circumference of 25.13 ft.?

181. What is the area of a lot of land of the dimensions shown in Fig. 78?

Fig. 78.

182. How many gallons of water may be contained in a cistern 10' in diameter, and 10' high? (See Table 29, page 216.)

183. How many gallons of water may be contained in a cistern 9' in diameter and 7' high?

184. What is the area of an irregular, four-sided floor the diagonals of which meet at right angles and are 70' and 39.889' respectively?

Suggestions for drill in the use of:

185. Signs of division.

(a)6÷3; (b) 12 ÷ 6; (c) 50÷2; (d) 60÷ 3; (e) 80÷ 4;

(f) 9:3; (g) 8:2; (h) 28:7; (i) 110: 11; (j) 36:9; (k) 50:25;

(I) 75: 15; (m)49/7; (n) 28/4; (o) 96/24; (p) 65/5; (q) 80/16;

(r)42/7;

(s)24/6; (t) 92/2; (u) 22/11;(v) 39/13; (w) 165/5.

186. Vinculum.

(a) 5+6 X 7; (6) 9-6 X 6.

Parenthesis.

(c) (6 + 10) X 9; (d) (5-3) X (6 + 9);

(e) (5 X 6) (7 - 5); (f) (6 + 18) 12.

Brackets.

(g) [9 + 12] x 6; (h) [7 - 3] X 12; (i) [6 + 4] X [5 - 1];

(j) [5 + 3] X 6. Brace.

(k) {6+5}x5; (I) {5+3}x2; (m) {4+6}x9; (n) {4 - 3} X 21.

187. Radical sign.

188. Use signs as follows:

(a) [(3 X 4) + 6] 2; (b) [(12 X 3÷ 4)x6];

(c) [(6+9 X 3 - 5) ÷ 4] X 12;

(6 X 5 X 3) ÷ 6;

Formulas.

189. What is the area of a rectangle 400' X 296'? Use the following formula in the solution of this problem.

L - length. W = width. A = area.

Formula A. A = L X W.

190. Find 1/2 of the cubic contents of a room 15 ft. long, 12 ft, wide, and 9 ft. high, using the following formula:

L = length. H = height.

W = width. C = cubic contents.

Formula B. C = L X W X H.

191. How many square feet of boards will be required to cover the two gables of a half pitch house which is 20' wide? Make no allowance for waste.

Area of a triangle.

B = base. H = height. A = area.

Formula C. A = B X H.

192. How many feet of boards will be required to cover the gables of a third pitch house which is 24' wide? Make no allowance for waste.

193. How many square feet are there in a room which is 30' upon one side, 35' upon the other, and 25' wide?

L = length of short side. W = width.

B = length of long side. A = area.

Formula D. A = L + B/2 W..

194. What is the area of an octagonal room which is 5' upon each side, and 6' 1/2" from the center to the side?

L = length of one side. N = number of sides. A = area. W = perpendicular distance from the center to the side.

Formula E. A = LNW/2.

195. Find the area of an irregular polygon, by the method indicated in Fig. 79.

Fig. 79.

196. Find the circumference of a circle which is 9' in diameter.

π = pi, the ratio of the diameter to the circumference, = 3.1416. C = circumference. R = radius. D = diameter.

Formula F. C = 2 πR = Dπ.

197. What is the diameter of a circle which is 39.27 ft. in circun erence?

Formula G. D = C/π.

198. What is the area of a circle which is 7' in diameter?

Formula H. A = D2.7854.

Another method. Formula I. A = πR2.

199. Find the diameter of a circle which is 314.16 sq. ft. in area.

Formula J. D =

200. What is the area of a circular wall 12' in diameter outside, and 9' inside?

201. Find the length of an arc of 24° which has a radius of 6'.

L = length of arc. R = radius.

N = number of degrees. C = circumference.

Formula K. L = RN/573.

Another method. Formula L. L = C/360 N.

202. What is the area of a circular auditorium which is 160' in diameter?

203. How many pupils could stand sideways around the wall, if each occupied approximately 12" of space, allowing 30.46' for openings?

204. If the ceiling of a hall 150' X 150' is 21.4377' above the floor, what are the cubic contents of the room? Omit fractions in the answer.

205. The walls of an auditorium, 120.58' square and 25' high, are to be plastered. How many square feet of wall space will have to bo covered if no allowance is made for openings?

206. What is the brick area of a wall which is 39.20' X 40' upon the outside, pierced with a circular hole which is 20' across?

The steel square is to be used as much as possible in the solution of the following problems.

207. If a building is 28' X 40', and the batter boards are 5' from each corner, what is the distance between their corners?

208. What will be the length of the diagonals of the above batter boards?

209. If a building is 24' X 32', what is the length of each diagonal?

210. What is the length of a brace completing a triangle, each of the two sides of which is 57" long?

211. What is the length of a brace completing a triangle, the sides of which are 6' and 8' long?

212. Allowing 2 1/2 tons per square foot for a safe load, what will a footing course 6' X 6' carry upon a bottom of hard clay?

213. A load of 300,000 lb. is to be supported upon a gravel bed, which will safely carry 8 tons per square foot. What should be the area of the foot of the pier?