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Brilio.net - Calculating the volume of geometric shapes is one of the important materials in Mathematics lessons, especially for grade 9 students. This material is not only useful for facing school exams, but also has real applications in everyday life. By understanding the basic concepts and the right formulas, calculating the volume of cylinders, cones, and spheres can be done easily and quickly.
Here is a complete review of examples of cylinder, cone, and sphere volume problems accompanied by complete steps to solve them. Each problem is designed to help students understand how the formula works and hone their arithmetic skills. In addition, these problems also include various variations to ensure a deeper understanding.
With regular practice and strong understanding, students will be more confident in facing various types of volume problems of geometric shapes. Let's look at the following examples of questions and learn how to solve them in detail, reported by brilio.net from various sources, Wednesday (5/2).
Volume example questions
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1. Volume of the Cylinder
Question 1: A cylinder has a radius of 7 cm and a height of 10 cm. Calculate the volume of the cylinder.
Solution: Formula for the volume of a cylinder: V = rtV = 3.14 7 10V = 3.14 49 10V = 3.14 490V = 1,538.6 cm
Answer: 1,538.6 cm
Question 2: A cylinder is known to have a diameter of 14 cm and a height of 15 cm. Calculate its volume.
Solution: Radius (r) = 14/2 = 7 cmV = rtV = 3.14 7 15V = 3.14 49 15V = 3.14 735V = 2,307.9 cm
Answer: 2,307.9 cm
2. Volume of Cone
Question 3: A cone has a radius of 6 cm and a height of 9 cm. Calculate its volume.
Solution: Cone volume formula: V = (1/3)rtV = (1/3) 3.14 6 9V = (1/3) 3.14 36 9V = (1/3) 1,017.36V = 339.12 cm
Answer: 339.12 cm
Question 4: A cone with a diameter of 10 cm and a height of 12 cm. Calculate its volume.
Solution: Radius (r) = 5 cmV = (1/3)rtV = (1/3) 3.14 5 12V = (1/3) 3.14 25 12V = (1/3) 942V = 314 cm
Answer: 314 cm
3. Volume of Ball
Question 5: Calculate the volume of a sphere with a radius of 7 cm.
Solution: Ball volume formula: V = (4/3)rV = (4/3) 3.14 7V = (4/3) 3.14 343V = (4/3) 1,077.62V 1,436.83 cm
Answer: 1,436.83 cm
Question 6: A ball has a diameter of 12 cm. Calculate its volume.
Solution: Radius (r) = 6 cmV = (4/3)rV = (4/3) 3.14 6V = (4/3) 3.14 216V = (4/3) 678.24V 904.32 cm
Answer: 904.32 cm
4. Combined Questions
Question 7: Calculate the volume of a cylinder with a radius of 4 cm and a height of 8 cm, then calculate the volume of a cone with the same dimensions. What is the difference in volume?
Solution: Volume of the cylinder: V = 3.14 4 8 = 3.14 16 8 = 402.12 cm
Volume of cone: V = (1/3) 3.14 16 8 = 134.04 cm
Volume difference: 402.12 - 134.04 = 268.08 cm
Answer: 268.08 cm
Question 8: A cylinder and a sphere have a radius of 5 cm. If the height of the cylinder is 10 cm, calculate the difference in volume.
Solution: Volume of the cylinder: V = 3.14 5 10 = 3.14 25 10 = 785 cm
Volume of sphere: V = (4/3) 3.14 125 = 523.33 cm
Volume difference: 785 - 523.33 = 261.67 cm
Answer: 261.67 cm
5. Application Questions
Question 9: A water tank is in the form of a cylinder with a diameter of 20 cm and a height of 50 cm. Calculate the maximum capacity of the tank.
Solution: Radius (r) = 10 cmV = 3.14 10 50V = 3.14 100 50V = 15,700 cm or 15.7 liters
Answer: 15.7 liters
Question 10: A toy ball has a radius of 3 cm. How many liters of air are needed to fill the ball?
Solution: V = (4/3) 3.14 3V = (4/3) 3.14 27V = 113.04 cm or 0.113 liters
Answer: 0.113 liters
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