Damirez Experiment 1

SOLID GEOMETRY 1. Find the volume of a right circular cylinder whose lateral area is 25.918 m2 and base area of 7.068 m2. a.

19.44 m3

c.

20.53 m3

b.

15.69 m3

d.

18.12 m3

2. A cylindrical tank open at the top is made of metal sheet having a total area of 49.48 m2. If the height of the tank is 1.5 times its base diameter, determine the base diameter of the tank. a.

3.5 m

c.

3m

b.

2.5 m

d.

3.2 m

3. The slant height of a right circular cone is 5 m long. The base diameter is 6 m. What is the lateral area in m2? a. b.

37.7 47

c. d.

44 40.8

a.

67 %

c.

69 %

b.

63 %

d.

65 %

8. A right circular cone with an altitude of 9 m is divided into two segments. One is a smaller circular cone having the same vertex with an altitude of 6 m. Find the ratio of the volume of the two cones. a.

1:3

c.

2:3

b.

19:27

d.

8:27

4.52 cm

c.

5.04 cm

b.

6.74 cm

d.

6.12 cm

a.

7,421

c.

4,721

b.

2,741

d.

1,321

14. The volume of a sphere is 52 m3. Determine its surface area in square meters.

9. A right circular cone with an altitude of 8 cm is divided into two segments. One is a smaller circular cone having the same vertex with volume equal to 1/4 of the bigger cone. Find the altitude of the smaller cone. a.

13. The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 2,744 cc. What volume in cc inside the shell is not occupied by the block?

a.

54.1

c.

56.32

b.

93.3

d.

67.35

15. Find the radius of the spherical wedge whose volume is 12 m3 with a central angle of 1.8 radians. a.

2.36 m

c.

2.52 m

b.

2.73 m

d.

2.15 m

a.

8 cm

c.

6 cm

10. An artificial lake, 5 m deep, is to be dug in the form of a frustum of an inverted pyramid. The level bottom is 8 m by 80 m and its top is 10 m by 100 m. How many cubic meters of earth is to be removed?

b.

9 cm

d.

10 cm

a.

4,067

c.

4,286

a.

9.67

c.

9.49

b.

4,417

d.

4,636

b.

9.85

d.

9.94

4. The lateral area of a right circular cone of radius 4 cm is 100.53 cm2. Determine the slant height.

5. The base diameter of a cone is 18 cm and its axis is inclined 60 with the base. If the axis is 20 cm long, what is the volume of the cone?

ANALYTIC GEOMETRY 16. Find the distance between (4, -2) and (-5, 1).

11. The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are 9 m and 3 m, respectively. If the volume is 118.2 m3, how far apart are the bases?

17. What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2 = 0. a.

y+x+4=0

c.

y–x–4=0

a.

9m

c.

7m

b.

y–x+4=0

d.

y+x–4=0

6. The base edge of a regular triangular pyramid is 12 m. If the altitude is 9 m, what is the volume in m3?

b.

8m

d.

10 m

a.

193.99

c.

187.06

12. The volume of sphere of radius 1.2 m is:

18. Find the angle that the line 2y – 9x – 18 = 0 makes with the X-axis.

b.

169.74

d.

180.13

a.

6,666 m3

c.

8,567 m3

b.

4,156 m3

d.

7.238 m3

a.

1,524 cc

c.

1,245 cc

b.

1,469 cc

d.

1,689 cc

7. If the edge of a cube is increased by 30%, by how much is the surface area increased?

a.

74.77

c.

47.77

b.

4.5

d.

77.47

19. The distance from the point (2, 1) to the line 4x – 3y + 5 = 0 is

b.

113

d.

138

a.

2

c.

1

27. Locate the center of the curve x2 + y2 + 8x + 4y – 61 = 0.

b.

4

d.

3

a.

(4, -2)

c.

b.

(-4, 2)

d.

20. Determine the distance from (5, 10) to the line x – y = 0. a.

3.86

c.

3.54

b.

3.68

d.

3.72

21. How far is the line 3x – 4y + 15 = 0 from the origin?

a.

14.2

c.

12.5

(4, 2)

b.

13.5

d.

15.2

(-4, -2)

35. Find the ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 72x – 24y – 144 = 0.

28. Where is the vertex of the parabola x2 = 4 (y – 2)? a.

(2, 0)

c.

(0, 4)

b.

(4, 0)

d.

(0, 2)

a.

1

c.

3

29. What is the length of the latus rectum of the curve x2 = 20y?

b.

2

d.

4

a.

5

c.

4

b.

20

d.

8

22. Where is the center of the curve x2 + y2 – 2x – 4y – 31 = 0? a.

(-1, -2)

c.

(1, 2)

30. What is the length of the latus rectum of the curve x2 = 12y?

b.

(1, -2)

d.

(-1, 2)

a.

12

c.

3

b.

-3

d.

-12

23. What is the radius of the circle x2 + y2 – 10x + 4y – 196 = 0? a.

15

c.

17

31. Determine the equation of the directrix of the curve x2 = 16y.

b.

16

d.

14

a.

x+4 = 0

c.

y–4 = 0

b.

x–4 = 0

d.

y+4 = 0

24. Determine the area enclosed by the curve x2 – 10x + 4y + y2 = 196. a.

15

c.

12

32. What is the area enclosed by the curve 9x2 + 25y2 – 225 = 0?

b.

225

d.

144

a.

188.496

b.

47.125

25. Find the center of the circle

x2

+

y2

– 6x + 4y – 23 = 0.

a.

(3, -2)

c.

(-3, 2)

b.

(3, 2)

d.

(-3, -2)

26. Find the area of the curve x2 + y2 + 6x – 12y + 9 = 0. a.

125

c.

92

c. d.

34. How far apart are the directrices of the curve 25x2 + 9y2 – 300x – 144y + 1251 = 0?

150.796

75.398

a.

0.67

c.

1.5

b.

1.8

d.

0.75

36. Find the area of the ellipse 25x2 + 16y2 – 100x + 32y = 284. a.

86.2

c.

68.2

b.

62.8

d.

82.6

37. Find the distance between the foci of the curve 9x2 + 25y2 – 18x + 100y – 116 = 0. a.

7

c.

8

b.

6

d.

12

38. Determine the latus rectum of the ellipse 49x2 + 36y2 + 392x – 216y – 656 = 0. a.

16.333

c.

13.215

b.

10.286

d.

9.456

39. Find the ratio of the length of the minor axis to the length of the major axis of the ellipse 9x2 + 16y2 – 144 = 0. a.

0.75

c.

0.43

b.

0.62

d.

0.58

33. Determine the length of the latus rectum of the curve 25x2 + 9y2 – 300x – 144y + 1251 = 0.

40. Determine the center of the hyperbola x2 – 2y2 + 4x + 4y + 4 = 0?

a.

3.2

c.

3.6

a. (-2,1)

c. (1,2)

b.

3.4

d.

3.0

b. (2,-1)

d. (-1,2)