Sold figures in Mathematics

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