Review Module 05 - Plane and Solid Geometry Part 2

MANILA: Room 206, JPD Building, CM Recto Avenue, Manila
CEBU: 4/F J. Martinez Bldg., Osmeña Blvd., Cebu City

o
Telephone Number: (02) 516 7559 (Manila) E-Mail: buksmarquez1 @yahoo.com
(032) 254-6697 (Cebu)
Review MODULE – Solid Geometry

SIMILAR SOLIDS 11. Find the volume of a frustum of a square pyramid if it has side dimension
𝑺𝟏 𝑷𝟏 𝑨𝟏 𝟏/𝟐 𝑽𝟏 𝟏/𝟑 of 15 and 20 cm on each base. The distance between the parallel bases is 18
= =( ) =( )
𝑺𝟐 𝑷𝟐 𝑨𝟐 𝑽𝟐 cm.
SITUATION. A trough whose ends are isosceles trapezoids is 8 m long, the

SITUATION. For a given solid, lower base is 4 m, the upper base is 6 m and the depth is 4m. The trough is
1. Determine the percentage increase in the diameter if the surface area
filled with 150 m3 of water.
increases by 30%
12. Compute the capacity of the trough.
2. Determine the percentage increase in the volume if the surface area
13. Compute the depth of the water.
increases by 30%.
14. Compute the wetted area of the trough.
3. A chair is to be made from prototype of mass 10 g with a scale of 1:8. SITUATION. A boy is fetching water into a spherical well that is initially full.
Solve the weight of the chair. One morning, he decided to take a bath so he had a pail of water from the well.
The maintenance man noticed that the water level decreased by 1.5 m. The
POLYHEDRONS next day, the water level decreased to 4.5 m after the boy fetched several pails
- A three-dimension figure composed of flat polygonal faces, of water. Assuming the tank is 12 m high, determine:
straight edges, and sharp corners (vertices). 15. The volume of water the boy had during the first day.
16. The volume of water the boy had during the second day
PLATONIC SOLIDS
Polyhedra Vertices Faces Edges Sides 17. A pyramid 20cm high with a square base having dimensions 8cm by 8cm
Cube 8 6 12 Square
is cut parallel to the base by a plane 7cm from the base. Find the ratio of
Tetrahedron 4 4 6 Triangle
Octahedron 6 8 12 Triangle the area of the new smaller base over the base of the original pyramid.
Dodecahedron 20 12 30 Pentagon
Icosahedron 12 20 30 Triangle SURFACE AREA OF SURFACE OF REVOLUTION
𝑺𝑨 = 𝟐𝝅𝒓 𝒙 𝑨𝒓𝒄 𝒍𝒆𝒏𝒈𝒕𝒉

SITUATION. A polyhedron has all its faces in a shape of an equilateral triangle.
The solid has 12 edges.
4. Name the polyhedron. 18. Determine the amount of material formed by rotating a 30 cm high line to
5. Determine the number of vertices a vertical axis 25 cm away parallel to the line.
SOLIDS WITH CONSTANT CROSS-SECTION VOLUME OF SOLID OF REVOLUTION
Examples: 𝑽 = 𝟐𝝅𝒓 𝒙 𝑨𝒓𝒆𝒂

Polygonal Prism
Right and Inclined Prism
Truncated Prism SITUATION. On top of a square is a semicircle whose diameter is equal to that
Volume: of the side of the square. Find the volume generated assuming that the radius
𝑉 = 𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎 𝑥 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ of the semicircle is 2m.
19. If the areas of this miscellaneous figure is rotated to an axis 0.88 m below
6. A truncated prism has a triangular base with sides 18 cm, 12, cm and 15 the bottom of the square.
cm. The vertical edges of the two corners are 30 cm and 25 cm, 20. If it is rotated 1 m to the left from the bottom of the square?
respectively. If the volume of the solid is 2232.35 cm3, determine the
length of the third vertical edge.
SITUATION. A prism has a base in the shape of a hexagon with each side
measuring 6 cm. The bases are 10 cm apart.
7. What is the volume of the right prism?
8. What is the lateral surface area of the prism?
SOLIDS WITH SIMILAR CROSS-SECTION
Examples:
Cone or Frustum of a Cone
Pyramid or Frustum of a Pyramid
Sphere or Frustum of a Sphere
Volume (General Prismoidal Formula):
𝐿
𝑉 = (𝐴1 + 4𝐴𝑚 + 𝐴2 )
6
9. A solid has a circular base of diameter 18cm. Find the volume of the solid
if every cutting plane perpendicular to the base along a given diameter is
an equilateral triangle
10. The base diameter of a cone is 20 cm, and its axis is inclined 60° with the
base. If the axis is 20 cm long, what is the volume of the cone?

Review Module 05 - Plane and Solid Geometry Part 2

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MANILA: Room 206, JPD Building, CM Recto Avenue, Manila

CEBU: 4/F J. Martinez Bldg., Osmeña Blvd., Cebu City

Review MODULE – Solid Geometry

SITUATION. A trough whose ends are isosceles trapezoids is 8 m long, the

𝑺𝑨 = 𝟐𝝅𝒓 𝒙 𝑨𝒓𝒄 𝒍𝒆𝒏𝒈𝒕𝒉

SOLIDS WITH CONSTANT CROSS-SECTION VOLUME OF SOLID OF REVOLUTION

Examples: 𝑽 = 𝟐𝝅𝒓 𝒙 𝑨𝒓𝒆𝒂

SOLIDS WITH SIMILAR CROSS-SECTION

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