This document discusses the volume computation of different solid figures including prisms, pyramids, cones, cylinders, and spheres. It provides examples of calculating the volume of each type of solid figure. For prisms, the volume is calculated as V=Bh, where B is the area of the base and h is the height. For pyramids and cones, the volume is calculated as V=1/3Bh. For spheres, the volume is calculated as V=4/3πr^3, where r is the radius of the sphere.

1. SOLID
FIGURESVolume Computation

2. Solid Figures
• Solid Figures are geometric figures with
length, height, and width.
• Also called as Three Dimension Figures.

3. Kinds of Solid Figures
• Prisms
• Pyramids and Cones
• Sphere

4. Prisms
• Prisms are solid figures with parallel
edges and uniform cross-sections.
• Right prisms are prisms with edges
perpendicular to the base.

5. Prisms
Examples of Prisms
• Cube
• Rectangular prism
• Triangular Prism

6. Prisms
• Right prisms with circular bases are referred to as
cylinders.

7. Pyramids and Cones
Pyramid
• A pyramid is a solid figure having a polygonal
base and triangular sides which meet in a point
called apex or vertex.

8. Pyramids and Cones
Cone
• A cone is a solid figure with a circle as a base.
Its lateral side is generated by a line through a
fixed point called vertex and a fixed curve plane
called the base.

9. Sphere
• A sphere is a solid figure with a set of points which
are equidistant from the center.

10. Volume Computation: Prisms
Prisms
• V=Bh , where ‘B’ as the area of the base.
Example 1:
Find the volume of a rectangular prism whose base is 12 ft by 4 ft
and 15 ft high.
Solution:
Area of the Base= lxw
=12 ft x 4 ft
= 48 ft2
Volume=Bxh
=48 ft2 x 15 ft
V=720 ft3

11. Volume Computation: Prisms
Example 2:
Find the volume of a cylinder with 6 inches in diameter and 12.5
inches long.
Solution:
B=r2
= 3.1416 x 32
=28.2744 sq.in.
V=Bxh
=28.2744 sq.in. x 12.5 in.
V=353.43 cu.in.

12. Volume Computation: Pyramids and Cones
Pyramids and Cones
• V=1/3Bh
Example 1:
Find the volume of a pyramid 18 1/2 inches high, the base of
which is rectangle 8 inches by 15 inches.
Solution:
B=lxw
=(15 in.)(8in.)
=120 sq.in.
V=1/3 Bh
=1/3(120 sq.in.)(18.5 in)
V=740 cu.in.

13. Volume Computation : Pyramids and Cones
Example 2:
Find the volume of the cone 12 in. high whose base is 6
in. diameter.
Solution:
B=3.1416 x (32)
=28.2744 sq. in.
V=1/3 B x h
=1/3 (28.2744sq.in.)(8 in.)
V=113.0976 cu.in.

14. Volume Computation: Sphere
Sphere
• V=4/3 πr3
Example:
Find the volume of an 8 cm. sphere.
Solution:
d=8cm
r=4cm.
V=4/3(3.1416)(43 )
V=268.0832 cu.in.

15. Assignment:
1. Define frustums
2. Draw example of frustums
Reference: Basic Mathematics( Second Edition)

16. Prepared by:
ARNEL B. MANCO