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Questions and Answers
What is the formula for finding the total surface area of a cone with base radius 'r' and slant height 'l'?
If the height of a cone is 15 cm and the slant height is 17 cm, what would be the base radius of the cone?
What is the relationship between the volume of a cone and the volume of a cylinder with the same base radius and height?
In the context of a cone, what does 'l' represent?
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In the given examples, what formula is used to calculate the volume of a cone?
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In Example 6, what would be the approximate total number of grains on the entire corn cob if each 1 cm^2 of its surface carries an average of six grains instead of four?
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For a cone with a height of 21 cm and a slant height of 28 cm, what is the base radius of the cone?
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What shape does the paper cut into little pieces along the slant height of the cone resemble?
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What is the formula for finding the total surface area of a cone according to the text?
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Why is it mentioned that in this chapter, 'cone' refers to a 'right circular cone'?
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Study Notes
Surface Area of a Cone
- The formula for finding the total surface area of a cone is: not provided in the given text
Dimensions of a Cone
- If the height of a cone is 15 cm and the slant height is 17 cm, the base radius of the cone can be calculated.
- For a cone with a height of 21 cm and a slant height of 28 cm, the base radius can be found.
Relationship between Cone and Cylinder
- The volume of a cone is related to the volume of a cylinder with the same base radius and height, but the exact formula is not provided in the given text.
Slant Height of a Cone
- In the context of a cone, 'l' represents the slant height.
Volume of a Cone
- The formula used to calculate the volume of a cone is not provided in the given text.
Real-World Application
- If each 1 cm^2 of a corn cob's surface carries an average of six grains, the approximate total number of grains on the entire corn cob can be calculated.
Properties of a Cone
- The paper cut into little pieces along the slant height of the cone resembles a sector.
Importance of Definition
- In this chapter, 'cone' specifically refers to a right circular cone.
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Description
This quiz explores the relationship between the volume of a cone and a cylinder. By filling and emptying the cone into the cylinder multiple times, observations are made to understand how many times the cone needs to be filled to completely fill the cylinder.
