Volume of Solid Figures

Volume of Solid Figures

1. Find the volume of cylinders, pyramids, cones and spheres. (M6ME-IVb-97)

2. Solve routine and non-routine problems involving volume of solids. (M6ME-IVc-98)

Expectations

After this lesson, you are expected to:

• Identify the different solid figures and their meaning.

• Apply the appropriate formula in solving the volume of a particular solid figure.

• Follow the proper steps in solving the problems

• Find the volume of different solid figures.

• Solve routine and non-routine problems, involving volume of solid figures -- cylinders, pyramids, cones and spheres.

Pre-test

Choose the letter of the correct answer. Write your answer on a separate sheet of paper. Use 3.14 for π and round off answer to the nearest hundredths.

Multiple Choice

1. What is the volume of a cylinder with a height of 12 centimeters and a radius of 3.4 cm?

• A. 434.58𝑐𝑚.³

• B. 435.58𝑐𝑚.³

• C. 436.58𝑐𝑚.³

• D. 437.58𝑐𝑚.³

Multiple Choice

2. A cone has a height of 9 inches and a radius of 6.3 inches. Find its volume.

• A. 373.88𝑖𝑛.³

• B. 373.97𝑖𝑛.³

• C. 373.87𝑖𝑛.³

• D. 374.89𝑖𝑛.³

Multiple Choice

3. Find the volume of a rectangular pyramid with a height of 12 centimeters, a width of 8 centimeters, and a length of 9 centimeters

• A.287𝑐𝑚.³

• B. 288𝑐𝑚.³

• C. 289𝑐𝑚.³

• D. 290𝑐𝑚.³

Multiple Choice

4. The radius of spherical container tank is 4 meters. How much water can it store?

• A. 267.97𝑚³

• B. 266.94𝑚³

• C. 267.95𝑚³

• D. 267.96𝑚³

Multiple Choice

5. A spherical ball is being inflated and reaches a diameter of 11 inches. What is the amount of air that the ball can hold?

• A. 699.56𝑖𝑛.³

• B. 698.55𝑖𝑛.³

• C. 697.46𝑖𝑛.³

• D.696.56𝑖𝑛.³

 Looking Back at your Lesson

Write TRUE if the statement is correct and FALSE if the statement is wrong.

Multiple Select

1. The volume of a sphere is  $\frac{2}{3}$  the volume of a cylinder.

• True

• False

Multiple Select

2. The volume of rectangular pyramid is  $\frac{2}{3}$  the volume of rectangular prism.

• True

• False

Multiple Select

3. The volume of a cone is  $\frac{2}{3}$ the volume of a cylinder.

• True

• False

Multiple Select

4. The volume of a sphere with a radius 1 is 4π .

• True

• False

Multiple Select

5. A cylinder with a radius 1 and height equal to 1 has a volume equal to  $\pi$ .

• True

• False

• Have you ever gone to a family outing to a resort? 

• There are many different kinds of swimming pool, isn’t it? There are swimming pools for kids and for adults. There is also Jacuzzi.

• If you will be asked how much water is placed in the swimming pool, how will you do it?

Which of the three pools in the picture occupies more space and why?

In this lesson you are going to learn about finding the volume of the solid figures. (cylinders, pyramids, cones and spheres)

Introduction

• What is volume? How volume is measured?

• Volume is the three-dimensional space enclosed by a boundary occupied by a certain object. The volume of an object is usually measured using cubic units.

Solid Figures and its Volume Formula

Prism

Prism is a solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms.

VOLUME OF CYLINDERS

A cylinder is a solid plane figure with two identical flat ends that are circular and one curved side. It has the same cross section from one end to the other. 

VOLUME OF PYRAMID

Pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is conic solid with polygonal base. A regular pyramid has a regular polygon base and is usually implied to be a right pyramid.

VOLUME OF CONES

Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface pointed towards the top. The pointed end of the cone is called the vertex, whereas the flat surface is called the base. 

VOLUME OF SPHERE

Sphere is a geometrical object in three dimensional space, that is, the surface of a ball. Like a circle in two dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance (r) from a given point in a three dimensional space. These are also referred to as the radius and center of the sphere respectively.