Math6 Quarter 4 Week 2 │Problem Solving involving Volume
Summary
TLDRThis educational video script delves into the concept of volume, explaining it as the measure of space occupied by solid figures. It covers the volume formulas for various shapes, including cubes, rectangular prisms, pyramids, cylinders, cones, and spheres. The script demonstrates how to calculate the volume of each shape with given dimensions, providing step-by-step examples for a rectangular prism, triangular prism, pyramid, cylinder, cone, and sphere. It also includes practical problems, such as calculating the volume of an ice cream cone and a water tank, and concludes with the volume of a cube-shaped chalkbox. The video aims to teach viewers how to solve volume problems in mathematics.
Takeaways
- 📏 Volume is the number of cubic units contained in a space figure.
- 📐 The formula for the volume of a cube is side³ or side × side × side.
- 📦 For a rectangular prism, the volume is length × width × height.
- 🗻 The volume of a square pyramid is (side² × height) / 3.
- 🔺 For a rectangular pyramid, the volume is (length × width × height) / 3.
- 🔵 A cylinder's volume is π × radius² × height.
- 🔺 The volume of a cone is (π × radius² × height) / 3.
- ⚪ The formula for the volume of a sphere is (4/3) × π × radius³.
- 📏 Example: The volume of a rectangular prism with dimensions 7 cm × 3 cm × 4 cm is 84 cubic cm.
- 📐 Example: The volume of a triangular prism with a base of 12 cm, a height of 16 cm, and a prism height of 30 cm is 2880 cubic cm.
Q & A
What is the definition of volume in mathematics?
-Volume is the number of cubic units contained in a space figure.
What is the formula for finding the volume of a cube?
-The formula for the volume of a cube is \( s^3 \) or side times side times side.
How do you find the volume of a rectangular prism?
-The formula for the volume of a rectangular prism is length times width times height.
What is the formula for the volume of a square pyramid?
-The formula for the volume of a square pyramid is \( s^2 \times \text{height} / 3 \).
How is the volume of a rectangular pyramid calculated?
-The formula for the volume of a rectangular pyramid is length times width times height divided by 3.
What is the formula for finding the volume of a cylinder?
-The formula for the volume of a cylinder is \( \pi \times \text{radius}^2 \times \text{height} \).
How do you calculate the volume of a cone?
-The formula for the volume of a cone is \( \pi \times \text{radius}^2 \times \text{height} / 3 \).
What is the formula for the volume of a sphere?
-The formula for the volume of a sphere is \( 4/3 \times \pi \times \text{radius}^3 \).
How do you find the volume of a rectangular prism with a length of 7 cm, width of 3 cm, and height of 4 cm?
-The volume is found by multiplying the length, width, and height: \( 7 \times 3 \times 4 = 84 \) cubic centimeters.
How is the volume of a triangular prism calculated?
-The formula for the volume of a triangular prism is base area times height of the prism. For a triangle base, the base area is \( \text{base} \times \text{height} / 2 \).
What is the volume of a triangular prism with a triangle base area of 96 square meters and a height of 30 meters?
-The volume is \( 96 \times 30 = 2880 \) cubic meters.
How is the volume of a rectangular pyramid with a length of 6 cm, width of 4 cm, and height of 5 cm calculated?
-The volume is \( 6 \times 4 \times 5 / 3 = 40 \) cubic centimeters.
How do you find the volume of a cylinder with a radius of 2.2 cm and a height of 14.6 cm?
-The volume is \( \pi \times 2.2^2 \times 14.6 \approx 221.88 \) cubic meters.
What is the volume of a cone with a radius of 6 cm and height of 10 cm?
-The volume is \( \pi \times 6^2 \times 10 / 3 \approx 376.8 \) cubic centimeters.
How do you calculate the volume of a sphere with a diameter of 30 cm?
-First, find the radius by dividing the diameter by 2, which is 15 cm. Then, use the formula \( 4/3 \times \pi \times 15^3 \approx 14130 \) cubic centimeters.
What is the volume of an ice cream cone with a diameter of 32 mm and height of 45 mm?
-The volume is \( \pi \times 16^2 \times 45 / 3 \approx 12057.6 \) cubic millimeters.
How many liters of water can a water tank with an interior height of 10 meters and diameter of 6 meters hold if it is half full?
-The tank's volume is \( \pi \times 3^2 \times 10 \approx 282.6 \) cubic meters, so half full it can hold approximately 141.3 cubic meters of water.
What is the volume of a pyramid with a base area of 84 square decimeters and height of 16 decimeters?
-The volume is \( 84 \times 16 / 3 = 448 \) cubic decimeters.
How do you find the volume of a chalk box with each edge measuring 18 cm?
-The volume is \( 18^3 = 5832 \) cubic centimeters.
Outlines
📚 Introduction to Volume Calculations
The script introduces the concept of volume in mathematics, explaining it as the number of cubic units contained within a space. It presents formulas for calculating the volume of various solid figures, including cubes, rectangular prisms, pyramids (both square and rectangular), cylinders, cones, and spheres. The script then demonstrates the application of these formulas through examples, starting with a rectangular prism with dimensions of 7 cm in length, 3 cm in width, and 4 cm in height, calculating its volume to be 84 cubic centimeters. It continues with the calculation of a triangular prism, a rectangular pyramid, a cylinder, a cone, and a sphere, providing step-by-step instructions and results for each.
🍦 Practical Applications of Volume Calculations
This paragraph extends the discussion on volume calculations to practical scenarios. It addresses how to calculate the volume of an ice cream cone given its diameter and height, resulting in a volume of 12057.6 cubic millimeters. It then explores the capacity of a water tank with a diameter of 6 meters and a height of 10 meters, determining how much water it can hold when half full, which is 141.2 cubic meters. The script also calculates the volume of a pyramid with a base area of 84 square decimeters and a height of 16 decimeters, finding it to be 448 cubic decimeters. Lastly, it computes the volume of a cube-shaped chalkbox with an edge length of 18 centimeters, which equals 5832 cubic centimeters. The paragraph concludes by emphasizing the importance of remembering these volume formulas for solving various mathematical problems.
Mindmap
Keywords
💡Volume
💡Cubic Units
💡Formula
💡Cube
💡Rectangular Prism
💡Pyramid
💡Cylinder
💡Cone
💡Sphere
💡Pi (π)
💡Problem Solving
Highlights
Introduction to the concept of volume as the number of cubic units contained in a space.
Volume formulas for different solid figures: cube, rectangular prism, square pyramid, rectangular pyramid, cylinder, cone, and sphere.
Calculation of the volume of a rectangular prism with dimensions 7 cm x 3 cm x 4 cm, resulting in 84 cubic centimeters.
Explanation of the volume formula for a triangular prism, involving the area of the triangular base and the height of the prism.
Volume calculation of a triangular prism with a base of 12, height of the triangle 16, and prism height 30, yielding 2880 cubic meters.
Rectangular pyramid volume formula application with dimensions 6 cm x 4 cm x 5 cm, resulting in 40 cubic centimeters.
Cylinder volume calculation using the formula with pi, radius, and height, resulting in 221.88 cubic meters.
Cone volume calculation with the formula involving pi, radius, height, and division by 3, resulting in 376.8 cubic centimeters.
Sphere volume calculation using the formula with pi, radius cubed, and division by 3, resulting in 14,130 cubic centimeters.
Problem-solving example: Calculating the volume of an ice cream cone with a diameter of 32 mm and height of 45 mm.
Calculating the volume of water a tank can hold when half-full, given its interior height and diameter.
Volume calculation of a pyramid with a base area of 84 square decimeters and a height of 16 decimeters.
Determining the volume of a chalkbox with each edge measuring 18 centimeters using the cube formula.
Emphasizing the importance of remembering volume formulas for various geometric shapes in problem-solving.
Encouragement for new viewers to subscribe and enable notifications for more math and science content.
Transcripts
[Music]
our subject
is mathematics 6.
our last topic is volume when we say
volume
it is the number of cubic units
contained in a space
figure these are the following formula
of volume for the different solid figure
for cube we have s
raised to 3 or side times side times
rectangular prism the formula is length
times weight times height
four pyramid for square pyramid we have
s squared times height divided by three
for rectangular pyramid
length times width times height divided
by 3
for cylinder pi radius squared times
height
for cone pi radius squared times height
divided by 3
and for sphere 4 pi
radius cubed divided by 3.
now let us find the volume of the
following figure
this figure is rectangular prism with
length of 7 centimeter width is 3
centimeter and height is 4 centimeter
the formula in finding the volume of
rectangular prism
is length times weight times height we
will substitute the value for us to find
the volume
so length is 7 centimeter width is 3
centimeter then
height is 4 centimeter so we will
multiply 7 times 3 times 4
is equal to 84 cubic centimeter so the
volume
of the rectangular prism is 84 cubic
centimeter
now let us find the volume of triangular
prism
the formula is base times height divided
by 2
times height general formula in finding
the volume of a prism is base times
height
since the base of this figure is
triangle we will find its base area with
the formula
of base times height divided by 2. the
first
h is for the height of a triangle and
the second h
is for the height of the prism
so we will substitute so the base of the
triangle
is 12 and the height of the triangle is
16
then divided by 2 the height of the
prism is
30 so 12 times 16 divided by 2
is equal to 96 then copy 30.
96 times 30 is equal to 2880
so the volume of this triangular prism
is 2880
cubic meter next is
rectangular pyramid the formula is
length times width times height divided
by 3
so the length is 6 width is 4 and height
is 5 so 6 times 4 times 5
is equal to 120 then divided by 3
is equal to 40. so the volume of this
rectangular pyramid is 40 cubic
centimeters
next is cylinder the formula is pi
radius squared times
height so let us substitute uh the value
of pi
is 3.14 radius is 2.2 then height
is 14.6 so following the order of
operations
exponent so 2.2 times 2.2 is equal to
4.84
then we will multiply 3.14 times 4.84
times 14.6 so it is equal to
221.88 thousand
four hundred ninety six hundred thousand
so let us uh round off or estimate this
a number to the nearest
hundredths so the answer is 221.88
cubic meters so since akata binance 8 i4
so remain among young 8 so the volume of
the cylinder is 221.88 cubic
meters next is cone
the formula is pi range squared times
height divided by
3. so let's substitute pi is 3.14
radius is six then height is ten then
divided by
three so first is six times six is equal
to
thirty six then multiply three point
fourteen times thirty six
times ten is equal to one thousand one
hundred
four then divided by 3 the answer is
376.8
so the volume of this cone is 376.8
cubic centimeters
then sphere the formula is 4 pi
radius cube divided by 3.
so substitute the value so pi is 3.14
then we have 15 since the given is
diameter
then the half of the diameter is the
rejuve so 30 divided by 2 is
15. so um
15 cubed so 15 times 15 times 15 is
equivalent to three thousand three
hundred
seventy five then multiply the three
four times three point fourteen times
three thousand three hundred seventy
five
is equal to forty two thousand three
hundred ninety
divided by three so the answer is
fourteen thousand one hundred
thirty so the volume of the sphere is
fourteen thousand one hundred thirty
cubic centimeters
now let's have a problem solving first
is an ice cream cone has a diameter of
32 millimeters
and the height of 45 millimeters what is
its
volume so we have the diameter then
height so the formula is pi radius
squared times
i divided by three so since given
diameter
and dagnassa formula i rejoice in young
diameter
since angliameter po i
twice of rejoice then radius is half of
the diameter
so substitute pi is 3.14
radius is 16. so 32 divided by 2 is 16.
then height is 45. so 16 times 16 is
equal to 256
then multiply 3.14 times 256 times 45
is equal to 36 172.8 divided by 3
so the volume of the ice cream cone is
12057.6
cubic millimeters second problem
a water tank has an interior height of
10 meters and a diameter of 6 meters
how many liters of water can it hold
half
full so the formula is pi radius squared
times height
so again given on diameter so we will
divide six
by two so angry is not an i3
so we have three point fourteen times
three squared times
ten so three times three is equal to
nine then multiply three point fourteen
times
nine times ten is equal to 282.6 cubic
meters so since again ups a problem i
how many liters of water can it hold
half full so kalahati lung
so i'm 282.6 cubic meters
so we will divide 282.6
divided by two so the answer is
one hundred forty one point three cubic
meters so on volume
water tank half full i141
141.2 cubic meters
a pyramid has a height of 16 decimeter
its base is 84 square decimeter
what is its volume so the formula
is base times height divided by three so
this is the general formula for pyramid
so since given a young base angle
and general formula so base is
84 then height is 16 multiply 84 times
16 is equal to
1344 divided by 3
the volume of the pyramid is 448 cubic
decimeters a chock box measures 18
centimeter
on each edge what is the volume of the
box so the formula
is s cube or side time side
times side so we have 18 raised to three
so we will multiply 18 by itself three
times
so 18 times 18 times 18 is equal to
5832 so the volume of the chalkbox is
5832 cubic centimeters
always remember this formula in solving
volume
so we have four cube rectangular prism
square pyramid rectangular pyramid
cylinder
cone and sphere
that's the end of our discussion for
today i hope you learned how to solve
volume thank you for watching if you are
new in our channel
please subscribe and click the
notification bell for more
math and science videos
Voir Plus de Vidéos Connexes
5.0 / 5 (0 votes)