Mathematics6 q4 Week1 v4

4
MATHEMATICS 6
4th Quarter
Week 1
LEARNING ACTIVITY SHEET

Division of Surigao del Sur
Disclaimer: This Learning Activity Sheet (LAS) is based from the Self-Learning
Modules, Learner’s Materials, Textbooks and Teaching Guides released by
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Competency: Determines the relationship of the volume between a
rectangular prism and a pyramid; a cylinder and a cone; and a cylinder
and sphere . M6ME – IVa-95
Objectives: At the end of the week, you shall have

o stated the relationship of the volume between a rectangular prism and a
pyramid; a cylinder and a cone; and a cylinder and sphere
o derived a formula in finding the volume of cylinders, pyramids, cones and
spheres
o related the relationship of the volume between a rectangular prism and
a pyramid; a cylinder and a cone; and a cylinder and sphere
Learner’s Tasks
Lesson Overview
The volume is the quantity of space occupied by a 3D object, measured in

cubic units.
The pictures below are examples of a three- dimensional objects.
linaojosephine.weebly.com
A pyramid is a three-dimensional object with triangles as faces and a polygon

base. The faces are the flat surfaces or sides and the face is the face at the bottom.
A prism is a three-dimensional object with two polygon bases that ate of the
same shape and size. The faces are rectangles.
So what is the relationship between the volume of a rectangular prism and a

pyramid of the same base and height?
2
If prism and pyramid are of the same bases and height, the pyramid occupy 1/3 the
space of the prism. These facts allow us to see a relationship between the volume of a
prism and the volume of a pyramid.
Finding the volume of rectangular prism

We are to find how much space is contained in the prism in finding volume. To
do this, we need to determine area of one of the base and multiply it by its height.
Volume of prism = l x w x h
Example 1 : Find the volume of the box at the right
Using the formula V = l x w x h , we have

= 5 cm x 12 cm x 5 cm
= 300 cm3
Thus the volume of the box is 300 cm3
Finding the volume of a pyramid

Volume of a pyramid = 1/3 ( area of the base) x height of the prism
Volume of pyramid = l x w x h
3
The volume of a pyramid is the amount of space inside the pyramid

It takes three pyramids to fill the rectangular box. The pyramid and the
rectangular prism have the same base and height
3
Example 2 : Find the volume of the pyramid at the right
Solution:
V=1(lxwxh)
3
= 1 x ( 12 ft x 12 ft x 15 ft)
3
= 1 x 2160
3
V = 720 ft3
So, the volume of the pyramid is 720 ft3
What is the relationship between the volume of a cylinder and that of a cone ?
apex
Circular base
A cylinder is a three-dimensional solid.
A cone is a three-dimensional geometric shape that tapers smoothly from flat, circular
base to a point called apex or vertex.
Finding the volume of a cylinder and a cone
Volume of a cylinder = area of the circular base x height

Area of a circular base = 𝜋𝑟 2
Height = h
Volume of a cylinder = 𝜋𝑟 2 h
Finding the volume of a cone ;

Based on the illustration above, there are 3 cones needed to fill the cylinder and
both have the same circular base and height.
So , volume of cone = 1/3 𝜋𝑟 2 h
Where : 𝜋 = 3.14, 𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠, ℎ = ℎ𝑒𝑖𝑔ℎ𝑡
Volume of a cone = 𝜋𝑟 2 h
3
4
Example 3 : Find the volume of the cone at the right
Solution : V = 𝜋𝑟 2 h
3
= 3.14 x 32 x 7
3
= 3.14 x 9 x 7
3
= 197.82
3
V = 65.94 m3
So, the volume of the cone is 65.94 m3.
What is the relationship between the volume of a sphere and a cylinder ?

A cylinder is a three-dimensional solid.
A sphere has a three-dimensional shape that looks like a ball.
A circle on the sphere with the same center as the sphere has an area of 𝜋𝑟 2 .
The volume of this cylinder would be the area of its base times its height, which is 𝜋𝑟 2 x
2r or 2 𝜋𝑟 3 . The sphere does not fill the whole cylinder. In fact, its volume is 2/3 of the
volume of the cylinder.
Volume of a sphere = 4 𝜋𝑟 3
3
Example 4 : Find the volume of the sphere at the right

Solution :
V= 4 𝜋𝑟 3
3
= 4 x 3.14 x 43
3
= 4 x 3.14.x 64
3
= 12.56 x 64
3
= 803.84
3
V = 267.95 in3
So, the volume of the sphere is 267.95 in3
5
Activity 1
Direction : Read each item carefully. Write True if the statement is true, and False if not
true. Write your answer on a separate sheet of paper.
1. The volume of the prism, is 1/3 of the volume of the pyramid.

2. When a prism and a pyramid have the same base and height, the volume of the
pyramid is 1/3 of the volume of the prism.
3. The volume of the cone is 1/3 of the volume of the cylinder if both have identical
heights with equal areas.
4. If cylinder and sphere have the same height , they also have the same volume.
5. The volume of the cylinder is 4/3 of the volume of the sphere.
Activity 2
Direction : Find the formula for finding the volume of the following figures. Write your
answer on a separate sheet of paper.
1. 4.
V = ________________
V = _____________________
2.
5.
V = ________________
3.
V = _____________________
V = ____________________
6
Activity 3
Direction : Answer the question in 2 to 3 sentences. Write your answer on a separate
sheet of paper.
1. What is the relationship between the volume of a rectangular prism and of a
pyramid with the same height and base ?
Formative Test
Direction : Read each item carefully. Choose the letter of the correct answer. Write the
letter of the correct answer on a separate sheet of paper.
1. What is the relationship of the volume of a cylinder and a sphere ?

A. The volume of the cylinder is the same as the volume of the sphere.
B. Sphere’s volume is 2/3 of the cylinder’s volume.
C. The volume of the cylinder is 2/3 of the volume of the sphere.
D. If cylinder and sphere have the same height, they also have the same
volume.
2. Anne wants to fill her aquarium with water. The aquarium measures 15 cm
length, 18 cm width and 10 cm height. Which of the formula is she going to use
to know the amount of water to be filled ?
A. V= 4 𝜋𝑟 3 C. V = l x w x h
3
B. V = 𝜋𝑟 2 D. V = 𝜋𝑟 2 h
3
3. Which of the following will be used to find the volume of a cone ?

A. V= 4 𝜋𝑟 3 C. V = l x w x h
3
B. V = 𝜋𝑟 2 h D. V = 𝜋𝑟 2
3
4. What is the relationship of the volume of a cylinder and a cone ?
A. If cylinder and a cone have the same heights and base, they also have the
same volume.
B. Cone’s volume is 2/3 of the cylinder’s volume.
C. Cylinder’s volume is 1/3 of the volume of the cone.
D. The volume of the cone is 1/3 of the volume of the cylinder if both have
identical heights and with equal areas.
5. A water tank is shaped like a cylinder. It is 20 meters tall and has a radius of 7
meters. How many cubic meters of water can the tank hold ? Which of the
following formula will be used ?
A. V= 4 𝜋𝑟 3 C. V = l x w x h
3
B. V = 𝜋𝑟 2 h D. V = 𝜋𝑟 2
3
7
Answer Key
Activity 1.
1. False
2. True
3. True
4. True
5. False
Activity 2.
1. 𝑉 = 𝜋𝑟 2 h
3
2. V = l x w x h
3. V = l x w x h
3
4. V = 𝜋𝑟 2
5. V= 4 𝜋𝑟 3
3
Activity 3
Pupils answer may vary
References
Grade 6 21st Century MATHletes pages 288 – 297.
Online Resource:
calcworkshop.com , onlinemath4all.com

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4

LEARNING ACTIVITY SHEET

Development Team Quality Assurance Team

Developer: Amorel P. Arreza Evaluator/s: Jeana O. Pagay

PSDS/DIC: Josephine Aroa Learning Area EPS:

LAS Graphics and Design Credits:

For inquiries or feedback, please write or call:

Department of Education – Division of Surigao del Sur

Telephone: (086) 211-3225

Objectives: At the end of the week, you shall have

The volume is the quantity of space occupied by a 3D object, measured in

A pyramid is a three-dimensional object with triangles as faces and a polygon

So what is the relationship between the volume of a rectangular prism and a

Finding the volume of rectangular prism

Example 1 : Find the volume of the box at the right

Using the formula V = l x w x h , we have

Finding the volume of a pyramid

The volume of a pyramid is the amount of space inside the pyramid

Finding the volume of a cylinder and a cone

Volume of a cylinder = area of the circular base x height

Finding the volume of a cone ;

So, the volume of the cone is 65.94 m3.

What is the relationship between the volume of a sphere and a cylinder ?

Example 4 : Find the volume of the sphere at the right

1. The volume of the prism, is 1/3 of the volume of the pyramid.

1. What is the relationship of the volume of a cylinder and a sphere ?

3. Which of the following will be used to find the volume of a cone ?

Grade 6 21st Century MATHletes pages 288 – 297.

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