Review Problems In Solid Geometry-1
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Review Problems In Solid Geometry-1 as PDF for free.
More details
- Words: 1,430
- Pages: 5
Loading documents preview...
REVIEW PROBLEMS IN SOLID GEOMETRY Situation 1:
Two identical closed conical tanks contain equal amount of liquid. The first tank has its base at the bottom while that of the second is at the top. The liquid in the first tank stands 3 m. deep.
1.
Determine the volume of the liquid in the tank. a. 33.51 m3 c. 23.14 m3 b. 28.17 m3 d. 21.99 m3
2.
Determine the depth of the liquid in the second tank if it has an altitude of 6 m. and a base radius of 2 m. a. 5.15 m c. 3.77 m b. 4.65 m d. 5.74 m
3.
Determine the weight of the liquid in quintals if its unit weight is 9.3 kN/m 3. a. 217.25 c. 204.52 b. 208.49 d. 221.78
Situation 2:
A spherical ball was completely immersed into an inverted right circular cone full of water. After the ball was removed, it was found out that the water surface had dropped 6 cm. below the top of the cone. The diameter of the cone is 12 cm. and its altitude is 36 cm.
4.
Which of the following gives the area of contact between the water and cone? a. 688 cm2 c. 645 cm2 b. 625 cm2 d. 673 cm2
5.
Which of the following gives the volume spilled out when the ball was placed inside the cone? a. 565.25 cm3 c. 522.15 cm3 b. 581.09 cm3 d. 571.77 cm3
6.
Which of the following gives the diameter of the spherical ball? a. 5.15 cm c. 10.30 cm b. 6.18 cm d. 9.67 cm
Situation 3:
A solid consists of a cone surmounted by a hemisphere. The volumes of these two are equal.
7.
Determiner the angle that the slant height of the cone makes with the horizontal. a. 26°34’ c. 14°02’ b. 63°26’ d. 75°57’
8.
Determine the total altitude of the solid if it has a slant height of 4.47 m. a. 6.0 m c. 4.0 m b. 5.1 m d. 4.7 m
REVIEW PROBLEMS IN SOLID GEOMETRY 9.
Determine the total surface area of the solid. a. 51.74 m2 c. 55.89 m2 b. 53.22 m2 d. 58.12 m2
Situation 4:
A sphere of radius 5 cm. and a right circular cone of base radius 5 cm. and height of 10 cm. stand on a horizontal floor.
10.
Determine the vertical distance of a plane from the horizontal floor so that it will cut the two solids into equal circular sections. a. 1.5 cm c. 2.6 cm b. 3.3 cm d. 2.0 cm
11.
Determine the volume of the spherical segment below the plane. a. 54.45 cm3 c. 66.23 cm3 3 b. 59.21 cm d. 68.50 cm3
12.
Determine the volume of the conical segment below the plane. a. 131.71 cm3 c. 127.76 cm3 b. 140.54 cm3 d. 156.89 cm3
Situation 5:
A trough whose end are isosceles trapezoid is 10 m. long. The lower base is 2 m., the upper base is 6 m. and the depth is 4 m. The trough contains 100,000 liters of liquid,
13.
Compute the depth of the liquid in the trough. a. 1.45 m c. 3.41 m b. 1.96 d. 2.90 m
14.
Compute the wetted area of the trough. a. 82.3 m2 c. 117.8 m2 2 b. 104.8 m d. 99.1 m2
15.
How many spherical balls of 2.4 diameter should be placed in the trough so that the liquid surface is at the top edge of the latter? a. 9 c. 6 b. 7 d. 8 Situation 6: A horizontal cylindrical tank has a radius of 600 mm and a length of 5 m. 16.
Determine the volume of the water in the tank if it is 7/8 full. a. 3.75 m3 c. 2.99 m3 b. 5.65 m3 d. 4.95 m3
17.
Determine the depth of water in the tank when it is in the horizontal position. a. 0.981 m c. 1.007 m b. 1.093 m d. 0.881 m
REVIEW PROBLEMS IN SOLID GEOMETRY 18.
Determine the depth of water in the tank when it is in the vertical position. a. 4.11 m c. 3.82 m b. 3.56 m d. 4.38 m
Situation 7:
One edge of a regular hexahedron is 24 cm. long.
19.
Which of the following gives the ratio of the volume to the surface area? a. 4 c. 3 b. 6 d. 2
20.
Which of the following gives the percentage increase of the volume if the edges are increased by 50%? a. 235.7% c. 265.1% b. 256.1% d. 237.5%
21.
Which of the following gives the percentage decrease of the surface area if the edges are decreased by 50%? a. 25% c. 75% b. 55% d. 45%
22.
How much percentage should the edges of a cube be increased to double its volume? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
23.
How much percentage should the edges of a cube be decreased so as to decrease its volume by 40%? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
24.
How much percentage should the edges of a cube be increased so as to increase its surface area by 25%? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
Situation 8:
The ratio of the surface area of sphere x to the surface area of sphere y is 4. The ratio of the volume of sphere y to the volume of sphere z is 3.
25.
Compute the ratio of the volume of sphere x to the volume of sphere z. a. 24 c. 26 b. 28 d. 25
26.
Compute the ratio of the surface area of sphere x to the surface area of sphere z. a. 7.50 c. 8.32 b. 8.89 d. 7.01
27.
Compute the ratio of the volume of sphere x to the volume of sphere y.
REVIEW PROBLEMS IN SOLID GEOMETRY a. b. Situation 9:
9 8
c. d.
5 6
The diameters of two spheres are in the ratio of 2:3 and the sum of their volumes is 1260 cu. m.
28.
What is the volume of the larger sphere? a. 927cu. m c. 829 cu. m b. 892 cu. m d. 972cu. m
29.
What is the radius of the smaller sphere? a. 4.1 m c. 4.8 m b. 3.7 m d. 3.2 m
30.
What is the sum of the surface areas of the spheres? a. 677.21 cm2 c. 633.89 cm2 2 b. 686.53 cm d. 656.61 cm2
Situation 10: A sphere has a surface area of 314.16 cm2. 31.
Determine the volume of the sphere. a. 521.5 cm3 c. 558.0 cm3 b. 531.7 cm3 d. 523.6 cm3
32.
Determine the percentage increase in the diameter if the surface area increases by 20%. a. 9.5% c. 9.0% b. 10.0% d. 8.5%
33.
Determine the percentage increase in the volume if the surface area increases by 20%. a. 37.2% c. 31.3% b. 36.5% d. 34.9%
34.
Determine the area of the lune if it has a subtended angle of 80°. a. 21.63π m2 c. 19.12π m2 2 b. 22.22π m d. 18.78π m2
35.
Determine the volume of the wedge if it has a subtended angle of 80°. a. 120.18 m3 c. 116.36 m3 b. 113.10 m3 d. 122.89 m3
Situation 11: The centers of two spheres having equal radii of 2 m. area 2 m. apart. 36.
Compute the volume common to the two spheres. a. 33.51 m3 c. 10.47 m3 b. 14.07 m3 d. 31.53 m3
REVIEW PROBLEMS IN SOLID GEOMETRY 37.
Compute the surface area common to the spheres a. 62.30 m2 c. 50.26 m2 b. 25.13 m2 d. 29.18 m2
38.
Compute the area of the common base of the spherical segment. a. 3pi m2 c. 4pi m2 b. 5pi m2 d. 6pi m2
Situation 12: A sphere has a diameter of 24 cm. 39.
How far from the center of the sphere should a plane be passed so that the ratio of the areas of the two zones formed is 2:3? a. 9.6cm c. 9.4 cm b. 2.6 cm d. 2.4 cm
40.
What is the ratio of the volume of the bigger to the smaller segment? a. 1.33 c. 1.93 b. 1.47 d. 1.84
41.
What is the volume of the spherical sector formed with the smaller segment? a. 926.1π cm3 c. 921.6π cm3 3 b. 931.6π cm d. 936.1π cm3
42.
A plane passes through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section. a. 3√2 sq. units c. 3√3 sq. units
Two identical closed conical tanks contain equal amount of liquid. The first tank has its base at the bottom while that of the second is at the top. The liquid in the first tank stands 3 m. deep.
1.
Determine the volume of the liquid in the tank. a. 33.51 m3 c. 23.14 m3 b. 28.17 m3 d. 21.99 m3
2.
Determine the depth of the liquid in the second tank if it has an altitude of 6 m. and a base radius of 2 m. a. 5.15 m c. 3.77 m b. 4.65 m d. 5.74 m
3.
Determine the weight of the liquid in quintals if its unit weight is 9.3 kN/m 3. a. 217.25 c. 204.52 b. 208.49 d. 221.78
Situation 2:
A spherical ball was completely immersed into an inverted right circular cone full of water. After the ball was removed, it was found out that the water surface had dropped 6 cm. below the top of the cone. The diameter of the cone is 12 cm. and its altitude is 36 cm.
4.
Which of the following gives the area of contact between the water and cone? a. 688 cm2 c. 645 cm2 b. 625 cm2 d. 673 cm2
5.
Which of the following gives the volume spilled out when the ball was placed inside the cone? a. 565.25 cm3 c. 522.15 cm3 b. 581.09 cm3 d. 571.77 cm3
6.
Which of the following gives the diameter of the spherical ball? a. 5.15 cm c. 10.30 cm b. 6.18 cm d. 9.67 cm
Situation 3:
A solid consists of a cone surmounted by a hemisphere. The volumes of these two are equal.
7.
Determiner the angle that the slant height of the cone makes with the horizontal. a. 26°34’ c. 14°02’ b. 63°26’ d. 75°57’
8.
Determine the total altitude of the solid if it has a slant height of 4.47 m. a. 6.0 m c. 4.0 m b. 5.1 m d. 4.7 m
REVIEW PROBLEMS IN SOLID GEOMETRY 9.
Determine the total surface area of the solid. a. 51.74 m2 c. 55.89 m2 b. 53.22 m2 d. 58.12 m2
Situation 4:
A sphere of radius 5 cm. and a right circular cone of base radius 5 cm. and height of 10 cm. stand on a horizontal floor.
10.
Determine the vertical distance of a plane from the horizontal floor so that it will cut the two solids into equal circular sections. a. 1.5 cm c. 2.6 cm b. 3.3 cm d. 2.0 cm
11.
Determine the volume of the spherical segment below the plane. a. 54.45 cm3 c. 66.23 cm3 3 b. 59.21 cm d. 68.50 cm3
12.
Determine the volume of the conical segment below the plane. a. 131.71 cm3 c. 127.76 cm3 b. 140.54 cm3 d. 156.89 cm3
Situation 5:
A trough whose end are isosceles trapezoid is 10 m. long. The lower base is 2 m., the upper base is 6 m. and the depth is 4 m. The trough contains 100,000 liters of liquid,
13.
Compute the depth of the liquid in the trough. a. 1.45 m c. 3.41 m b. 1.96 d. 2.90 m
14.
Compute the wetted area of the trough. a. 82.3 m2 c. 117.8 m2 2 b. 104.8 m d. 99.1 m2
15.
How many spherical balls of 2.4 diameter should be placed in the trough so that the liquid surface is at the top edge of the latter? a. 9 c. 6 b. 7 d. 8 Situation 6: A horizontal cylindrical tank has a radius of 600 mm and a length of 5 m. 16.
Determine the volume of the water in the tank if it is 7/8 full. a. 3.75 m3 c. 2.99 m3 b. 5.65 m3 d. 4.95 m3
17.
Determine the depth of water in the tank when it is in the horizontal position. a. 0.981 m c. 1.007 m b. 1.093 m d. 0.881 m
REVIEW PROBLEMS IN SOLID GEOMETRY 18.
Determine the depth of water in the tank when it is in the vertical position. a. 4.11 m c. 3.82 m b. 3.56 m d. 4.38 m
Situation 7:
One edge of a regular hexahedron is 24 cm. long.
19.
Which of the following gives the ratio of the volume to the surface area? a. 4 c. 3 b. 6 d. 2
20.
Which of the following gives the percentage increase of the volume if the edges are increased by 50%? a. 235.7% c. 265.1% b. 256.1% d. 237.5%
21.
Which of the following gives the percentage decrease of the surface area if the edges are decreased by 50%? a. 25% c. 75% b. 55% d. 45%
22.
How much percentage should the edges of a cube be increased to double its volume? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
23.
How much percentage should the edges of a cube be decreased so as to decrease its volume by 40%? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
24.
How much percentage should the edges of a cube be increased so as to increase its surface area by 25%? a. 15.7% c. 23.1% b. 26.0% d. 11.8%
Situation 8:
The ratio of the surface area of sphere x to the surface area of sphere y is 4. The ratio of the volume of sphere y to the volume of sphere z is 3.
25.
Compute the ratio of the volume of sphere x to the volume of sphere z. a. 24 c. 26 b. 28 d. 25
26.
Compute the ratio of the surface area of sphere x to the surface area of sphere z. a. 7.50 c. 8.32 b. 8.89 d. 7.01
27.
Compute the ratio of the volume of sphere x to the volume of sphere y.
REVIEW PROBLEMS IN SOLID GEOMETRY a. b. Situation 9:
9 8
c. d.
5 6
The diameters of two spheres are in the ratio of 2:3 and the sum of their volumes is 1260 cu. m.
28.
What is the volume of the larger sphere? a. 927cu. m c. 829 cu. m b. 892 cu. m d. 972cu. m
29.
What is the radius of the smaller sphere? a. 4.1 m c. 4.8 m b. 3.7 m d. 3.2 m
30.
What is the sum of the surface areas of the spheres? a. 677.21 cm2 c. 633.89 cm2 2 b. 686.53 cm d. 656.61 cm2
Situation 10: A sphere has a surface area of 314.16 cm2. 31.
Determine the volume of the sphere. a. 521.5 cm3 c. 558.0 cm3 b. 531.7 cm3 d. 523.6 cm3
32.
Determine the percentage increase in the diameter if the surface area increases by 20%. a. 9.5% c. 9.0% b. 10.0% d. 8.5%
33.
Determine the percentage increase in the volume if the surface area increases by 20%. a. 37.2% c. 31.3% b. 36.5% d. 34.9%
34.
Determine the area of the lune if it has a subtended angle of 80°. a. 21.63π m2 c. 19.12π m2 2 b. 22.22π m d. 18.78π m2
35.
Determine the volume of the wedge if it has a subtended angle of 80°. a. 120.18 m3 c. 116.36 m3 b. 113.10 m3 d. 122.89 m3
Situation 11: The centers of two spheres having equal radii of 2 m. area 2 m. apart. 36.
Compute the volume common to the two spheres. a. 33.51 m3 c. 10.47 m3 b. 14.07 m3 d. 31.53 m3
REVIEW PROBLEMS IN SOLID GEOMETRY 37.
Compute the surface area common to the spheres a. 62.30 m2 c. 50.26 m2 b. 25.13 m2 d. 29.18 m2
38.
Compute the area of the common base of the spherical segment. a. 3pi m2 c. 4pi m2 b. 5pi m2 d. 6pi m2
Situation 12: A sphere has a diameter of 24 cm. 39.
How far from the center of the sphere should a plane be passed so that the ratio of the areas of the two zones formed is 2:3? a. 9.6cm c. 9.4 cm b. 2.6 cm d. 2.4 cm
40.
What is the ratio of the volume of the bigger to the smaller segment? a. 1.33 c. 1.93 b. 1.47 d. 1.84
41.
What is the volume of the spherical sector formed with the smaller segment? a. 926.1π cm3 c. 921.6π cm3 3 b. 931.6π cm d. 936.1π cm3
42.
A plane passes through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section. a. 3√2 sq. units c. 3√3 sq. units
Related Documents
Review Problems In Solid Geometry-1
January 2021 0
Review Problems In Dc Motors
February 2021 13
Solid Mensuration Problems
January 2021 0
Ce Board Problems In Solid Geometry
February 2021 0
Problems In Malvino
February 2021 0
Economics_fe Review Problems And Solutions 2012
February 2021 0More Documents from "Blake Reeves"
Review Problems In Solid Geometry-1
January 2021 0
1920-1-acco 20073- Payroll Worksheet.xlsx
February 2021 0
1st-grading-exam.docx
February 2021 0
Arma Systems
January 2021 0
Genbio2_iiicg12_tmayugba
March 2021 0