The document describes a circular concrete conduit that is 1 ft thick with an inside diameter of 10 ft. The conduit rises 16 ft per 1000 horizontal ft. It has ends that are 3000 ft apart. The question asks to calculate the amount of concrete used to construct this conduit.

1. A circular concrete conduit, whose inside
diameter is 10 ft., is 1 ft. thick. It rises 16 ft.
per 1000 horizontal feet. The vertical plane
which contains the axis is perpendicular to
the two vertical planes which contain the
ends of the conduit. If the ends are 3000
ft. apart, find the amount of concrete used
in the construction of the conduit.

2. a. 103,685.69 ft 3
b.104,675.69 ft 3
c. 105,655.69 ft3
d.106,665.69 ft3

3. Solution:

5. Find the area of the largest circle
which can be cut from a square of
edge 4 inches. What is the area of the
material wasted?
a. 3.43 in2 c. 4.93 in2
b.5.43 in2 d.2.43 in2

6. A pine log 40 ft long has a uniform
circular cross section of radius 11 in.
the ends lie in parallel planes which are
not perpendicular to the axis of the log.
How much paint will be required to give
the log (ends not include) two coats. If 1
gal of paint covers 800 sq ft of surface?
If pine weighs 31 lb per cu ft. find the
weight of the log.

7. a. 3256.23 lb
b.3273.37 lb
c. 3569.23 lb
d.3965.12 lb

8. A cubic foot of water weighs about
62.4 lb. what must be the diameter
of a cylindrical pail 1 ft high in order
for it to hold the water from 25 lb of
ice? How many square inches of
sheet tin are required to make the
pan?

9. a. 380.74 in2
b.379.74 in2
c. 381.74 in 2
d.382.74 in 2

10. Find the waste in making the largest
possible cylindrical rod from a bar of
iron 3 ft long which has a square
cross section whose diagonal is 6 in.
a. 0.08048 ft3 c. 0.08566 ft3
b.0.09068 ft3 d.0.05698 ft3

11. If the edge of a cube is
increased by 30%, by how
much is the surface area
increased?
a. 30% c. 60%
b.33% d.69%

12. Solution:
Thus, A2 is increased by 69%

13. How many times do the
volume of a sphere
increases if the radius is
doubled?
a. 4 times c. 6 times
b.2 times d.8 times

14. Solution:
Thus, V2 is increased by 8 times

15. A conical vessel has a height of 24
cm and a base diameter of 12 cm.
it holds water to a depth of 18 cm
above its vertex. Find the volume
(in cm3) of its content
a. 188.40 c. 381.70
b. 298.40 d. 412.60

16. Solution:
r = 4.5

17. Building blocks are closely stacked
in a pile 7 ft. high, 36 ft. long and
12 ft. wide. If the bricks are 2 in.
by 4 in. by 9 in., how many bricks
are in the pile?
a. 73, 589 c. 74, 369
b. 72, 576 d. 75, 345

18. Solution:
For pile:
For one brick:

20. A trench is 180 ft. long and 12 ft
deep, 7 ft wide at the top and 4 ft
at the bottom. How many cubic
yards of earth have been
removed?
a. 440 c. 443
b. 442 d. 446

21. Solution:

22. A regular triangular pyramid
has an altitude of 9 m and a
volume of 187.06 cu.m.
what is the base edge in
meters?
a. 12 c. 14
b. 13 d. 15

23. Solution:

24. What is the volume of frustum of a
cone whose upper base is 15 cm in
diameter and lower base 10 cm in
diameter with an altitude of 25 cm.
a. 3018.87 cm3 c. 3108.87 cm3
b. 3180.87 cm3 d. 3081.87 cm3

25. Solution:

26. The volume of the frustum of a regular
triangular pyramid is 135 cu. m. The
lower base is an equilateral triangle
with an edge of 9 m. The upper base is
8 m above the lower base. What is the
upper base edge in meters?
a. 2 c. 4
b. 3 d. 5

27. Solution: