W8
Name
Grade Level
Learning Area/Quarter
May 17-21, 2021
Date
MATHEMATICS/THIRD QUARTER
VI- AQUAMARINE
Determining the Relationship of the Volume of the Solid Figures
Relationship of the volume between rectangular prism and pyramid
- The volume of pyramid is exactly 1/3 of the volume of a prism with exactly the same
bases and height
The volume of prism is the amount of space inside the
prism.
Volume is measured in cubic units, which means it tells
you how many cubes of a given size it takes to fill the
prism. We can use the diagram on page 288 to show
why the formula of any prism works.
base
)
height (h)
To find the volume (V) of a prism, multiply the number
of cubic units needed to cover the base (B) by the
number of layers (h).
So, for any prism,
Volume (V) = base area (B) x height (h)
Volume of prism
The Volume (V) of a prism is the product of
the base area (B) and the height (h).
V=B∙h
Since B=L∙W, then V=l∙w∙h
Example 1 Find the volume of the refrigerator
Solution
The refrigerator at the right is a
Rectangular prism.
Using the formula, V=l∙w∙h, we have:
V= l∙w∙h
= (3m) (2m) (6m)
V= 36𝒎𝟑
Thus, the volume of the
refrigerator is 36𝒎𝟑
The volume of pyramid is the amount of space inside the
pyramid. Volume measured in cubic units, which means
it tells us how many cubes of a given size it takes to fill
the pyramid.
It takes three pyramids of popcorn
to fill the rectangular box. The pyramid
and the rectangular prism have the same
base and height.
Example 2: Complete the statement.
Volume of the pyramid = _____ x volume of rectangular
Prism
For a rectangular prism, V= l x w x ______
So for pyramid, V= ____l x w or V =
1
3
𝑙𝑥𝑤𝑥ℎ
?
The volume of a pyramid is the volume of a prism
with same base area (B) and height (h)
Volume of pyramid
1
The formula for the volume of a pyramid is 3
the base area (B) times the height (h)
1
𝟏
V= 3 ∙ B ∙ h or V= 𝟑 (l∙w∙h)
Example 3: Find the volume of
the pyramid at the right.
Solution:
1
V= 3 (l∙w∙h)
1
= 3 x 62x40x50
1
= 3 x 124 000
V= 41 333.3 𝒎𝟑
Relationship of the volume between rectangular cylinder and cone
- The volume of a cone means the third part of the volume of a cylinder having the same
base and same height.
The volume of cylinder is the amount of space inside
the cylinder.
Finding the volume of a cylinder is similar to finding the
volume of any other prism.
Volume of Cylinders
The Volume (V) of a cylinder is the product of
the circular base (B) and height (h)
V= 𝝅 ∙ 𝒓𝟐 ∙ 𝒉
Example 4: Find the volume of coffee in this mug at the right.
Solution:
V= 𝝅 ∙ 𝒓𝟐 ∙ 𝒉
=3.14 x 62 x 12
= 3.14 x 36 x 12
V = 1356.48 cm 3
So, the volume of this mug is 1356. 48 cm 𝟑
Volume of Cone
At Five-Six convenience store, you can buy a Big Gulp
or a Little Gulp juice. The Big Gulp comes in a can, while the
Little Gulp is served in a cone.
How many bases does a cone have? What is the
shape of the base of the cone?
The Big
Gulpofcontainers
have equal radii
volume
cone
(plural for
radius)
and
equal
heights.
At five-six convenience
store, you can buy a Big Gulp or a Little Gulp Juice. The Big Gulp comes in a can,
So,
it
takes
three
Little
Gulps
to
while the Little Gulp is served infill
a one
coneBig Gulp.
What fraction of the volume of the Big Gulp is the volume of the Little Gulp?
The volume of cone is
1
3
of the volume of a cylinder with same base area (B) and height (h)
Volume of Cones
1
The Formula for the cone of a cone is 3 the base area (B) times the height (h)
𝟏
𝟑
V= ∙ B∙ h or V=
Example 5: Find the volume of the cone at the right.
Solution:
𝟏
𝟑
∙ 𝝅𝒓𝟐 ∙ 𝒉