Volume Relationship between Cone and Cylinder
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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'?

  • $ ext{Base Area} + ext{Curved Surface Area}$
  • $rac{1}{2} imes ext{Base Perimeter} imes ext{Slant Height}$
  • $ ext{Curved Surface Area} + ext{Base Area}$ (correct)
  • $rac{1}{2} imes ext{Base Area} + ext{Perimeter of Base} + ext{Slant Height}$

    • 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?

  • 6 cm
  • 12 cm
  • 8 cm (correct)
  • 10 cm

    • What is the relationship between the volume of a cone and the volume of a cylinder with the same base radius and height?

  • The volume of a cone is twice the volume of the cylinder.
  • The volume of a cone is one-third the volume of the cylinder. (correct)
  • The volume of a cone is equal to the volume of the cylinder.
  • The volume of a cone is half the volume of the cylinder.

    • In the context of a cone, what does 'l' represent?

    <p>Slant height</p> Signup and view all the answers

    In the given examples, what formula is used to calculate the volume of a cone?

    <p>$V = \frac{1}{3} \pi r^2 h$</p> Signup and view all the answers

    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?

    <p>640</p> Signup and view all the answers

    For a cone with a height of 21 cm and a slant height of 28 cm, what is the base radius of the cone?

    <p>7 cm</p> Signup and view all the answers

    What shape does the paper cut into little pieces along the slant height of the cone resemble?

    <p>Triangle</p> Signup and view all the answers

    What is the formula for finding the total surface area of a cone according to the text?

    <p>$rac{1}{2} imes l imes$ length of entire curved boundary</p> Signup and view all the answers

    Why is it mentioned that in this chapter, 'cone' refers to a 'right circular cone'?

    <p>To simplify the study by focusing on one type of cone</p> Signup and view all the answers

    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.

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