734
No. 24.
CLASS II.
GEOMETRY.
1. What is an angle? What is an acute angle? What do you understand by a plane? What are radii ?
What is a triangle ?
2. Write the supplement and the complement of the following angles :- 83°, 42o, 15', 49° 33′ 17′′, 51° 23′′.
3. Prove that the bisectors of the adjacent angles which one straight line makes with another contain a right angle.
4. Prove that any two sides of a triangle F. G. II. are together greater than the third side.
5. Show that the triangle formed by joining the middle points of the sides of au equilateral triangle is also equilateral.
No. 25.
CLASS I.
MENSURATION.
(Note-Assume r=31416.)
1. In a circular riding school of 150 feet in diameter, a circular ride, within the outer edge, is to be made of a uniform width of 12 feet: find the cost of doing this at 2s. 24d. per square yard.
2. The area of a quadrilateral is 37 acres 1 rood 16 poles; one diagonal is 25 chains find the sum of the perpendiculars on this diagonal from the two opposite angles.
3. Lay down the field A B C D E F G and find its area from the following dimensions:—
to⚫ T)
1560
G 690
864 618
20 E
from · F
to G
1305
D 690
363
from C
+
to · C
1650
B 362
1230
405
Begin
at +
A
390 G rauge East.
4. Find to the nearest gallon the quantity of water which will be held by a cylindrical vessel having the radius of its base 23 inches and its height being 22 inches.
What will be the weight of this quantity of water? (A cubic inch of water weighing 252.458 grains.)
5. Find the weight of an iron dumb-bell consisting of two spheres of 3 inches diameter joined by a cylindrical bar 6 inches long and 1 inch in diameter; an iron ball 4 inches in diameter weighing 9 lbs.
6. Find in cubic feet and decimals the volume of a triangular pyramid 8 feet in height and having its sides at the base 5, 7, and 9 feet in length,
7. Find the volume of a circular cone the height of which is 17 fect and the circumference at the base 22 feet.
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