Example of SLO-Based
Learning and Examination:
SLO: “Students shall be able to calculate the volume of a sphere using day-to-day environments.
To apply this SLO, students might engage with the following questions:
These types of questions not only assess a student’s ability to perform calculations but also their understanding of the concepts behind the calculations and their ability to apply these concepts in
real-life scenarios.
At CHACE, our commitment is to ensure that our students are not just well-prepared for exams but are also ready to tackle the challenges of practical life. We are dedicated to empowering them to
achieve academic excellence and contribute meaningfully to society, preparing
them for both national and international success.
Example of SLO-Based Learning and Examination:
SLO: “Students shall be able to calculate the volume of a sphere using day-to-day environments.
To apply this SLO, students might engage
with the following questions:
Practical Application Question:
At home, you have a spherical water tank that you suspect isn’t holding as much water as advertised. Using a measuring tape to find the radius and the formula for the volume of a sphere (V = 4/3 π r^3), calculate the actual volume of your water tank.
Conceptual Understanding Question:
Explain why the formula for the volume of a sphere is V = 4/3 π r^3. Identify what each component of the formula represents, particularly focusing on how π and r^3 contribute to calculating the volume.
Real-World Problem-Solving Question:
If the spherical water tank needs to be filled completely, and you know the flow rate of your water hose is 10 liters per minute, calculate how long it will take to fill the tank. Use the tank’s radius of 2 meters for your calculation.
Practical Application Question:
You have a rubber ball at home that you use for playing. Using a measuring tape and the formula for the volume of a sphere (V = 4/3 π r^3), calculate the volume of your ball.
1. Conceptual Understanding Question:
Explain why the formula for the volume of a sphere is given by V = 4/3 π r^3. What do each of the components in this formula represent?
2. Real-World Problem-Solving Question: If
you were to fill the ball with water, how much water would it hold? Use the diameter of the ball as 10 cm in your calculation.
These questions encourage students not only to perform mathematical calculations but also to deepen their understanding of geometric concepts and apply them to solve practical problems they might encounter in their everyday lives. This approach demonstrates the direct application of theoretical knowledge in practical scenarios, reinforcing the importance of conceptual learning in the SLO-based education system at CHACE.
MCQs:
What is the formula to calculate the volume of a sphere?
- A) V = πr^2
- B) V = 2/3 πr^3
- C) V = 4/3 πr^3
- D) V = πr^3
- Correct Answer: C
If the radius of a sphere is doubled, how does the volume change?
- A) Doubles
- B) Triples
- C) Quadruples
- D) Increases eightfold
- Correct Answer: D
What does the variable ‘r’ represent in the formula for the volume of a sphere?
- A) Diameter
- B) Circumference
- C) Radius
- D) Area
- Correct Answer: C
Which of the following is not a direct application of the volume formula of a sphere?
- A) Calculating the amount of air in a
- balloon
- B) Calculating the surface area of a ball
- C) Determining how much water a spherical
- tank can hold
- D) Finding out how much material is needed
- to make a shot put
- Correct Answer: B
Pi (π) in the formula of the volume of a sphere is approximately:
- A) 2.22
- B) 3.14
- C) 4.13
- D) 5.15
Correct Answer: B
Which unit could be used to express the volume of a sphere?
- A) Square meters
- B) Cubic meters
- C) Meters
- D) Kilograms
Correct Answer: B
If the radius of a spherical tank is 5 meters, what is its approximate volume? Use π = 3.14.
- A) 157 m³
- B) 314 m³
- C) 523.33 m³
- D) 785 m³
Correct Answer: C
The volume of a sphere is given as 904.32 cubic meters. If π = 3.14, what is the approximate radius?
- A) 7 m
- B) 6 m
- C) 5 m
- D) 4 m
Correct Answer: B
What happens to the volume of a sphere if the radius is halved?
- A) It is halved
- B) It reduces to a quarter
- C) It reduces to an eighth
- D) It stays the same
Correct Answer: C
Which formula is used for calculating the volume of a sphere in an exam if the radius is known?
- A) V = πr^2h
- B) V = 1/3 πr^2h
- C) V = 4/3 πr^3
- D) V = πr(h^2 + r^2)
Correct Answer: C
Numerical Problems:
Calculate the volume of a spherical water tank whose diameter is 10 meters. Use π = 3.14.
Solution:
Radius, r = Diameter / 2 = 10 m / 2 = 5 m
Volume, V = 4/3 πr^3 = 4/3 * 3.14 * (5)^3 ≈
523.33 m³
A spherical tank is filled at a rate of 12 liters per minute. If the tank has a volume of 2000 liters, how long will it take to fill it completely?
Solution:
Volume = 2000 liters
Rate = 12 liters/minute
Time = Volume / Rate = 2000 / 12 ≈ 166.67
minutes
These questions and solutions cover a range of difficulties and applications, helping students to understand and master the concept of calculating the volume of spheres in practical contexts.
Revised Numerical Problem:
Calculate the volume of a spherical water tank whose diameter is 4 meters. Use π = 3.14.
Solution:
Radius, r = Diameter / 2 = 4 m / 2 = 2 m
Volume, V = 4/3 πr^3 = 4/3 * 3.14 * (2)^3 ≈
33.51 m³
This adjusted calculation reflects the volume of a spherical tank with a smaller, more realistic diameter for typical residential use.
To solve the problem related to the pumping capacity of a 1-horsepower pump and calculate how long it would take to fill the spherical water tank with a volume of 33.51 cubic meters (33,510 liters, since 1 cubic meter = 1000 liters), we need to know the pumping rate of a 1-horsepower pump in liters per minute.
General Information:
1 horsepower (HP) can typically pump about 50 gallons per minute in standard conditions for water (1 gallon = 3.78541 liters).
Calculation:
Convert horsepower to liters per minute:
Pumping rate in gallons per minute for 1 HP = 50 gallons/min
Conversion to liters: 50 gallons/min × 3.78541 = 189.27 liters/min
Calculate time to fill the tank: Volume of tank = 33,510 liters
Pumping rate = 189.27 liters/min
Time to fill tank = Volume of tank / Pumping rate
Time = 33,510 liters / 189.27 liters/min ≈
177.05 minutes
Solution:
It would take approximately 177.05 minutes, or about 2 hours and 57 minutes, to fill a 4-meter diameter spherical water tank using a 1-horsepower pump with a pumping rate of 189.27 liters per minute.
This calculation provides an estimate based on typical pump capacities and assumes optimal conditions without accounting for any potential losses or variations in actual pump performance.
