[Q4] RELATIONSHIPS OF VOLUMES OF GEOMETRIC SOLIDS (M6ME-IVa-95)

Topic: Relationships of Volume in Geometric Solids (M6ME-IVa-95)

 PJ MIANA



1. Relationship between a Rectangular Prism and a Pyramid:

- A rectangular prism is a three-dimensional shape with six rectangular faces.

- Its volume (V) is given by the formula: V = length × width × height.

- A pyramid is a three-dimensional shape with a polygonal base and triangular faces meeting at a common vertex.

- The volume of a pyramid (V) is calculated using the formula: V = (1/3) × base area × height.

- In comparing the volumes of a rectangular prism and a pyramid:

  - If they have the same base area and height, the rectangular prism will have three times the volume of the pyramid.

  - This is because the rectangular prism fills up space more efficiently due to its shape.

 

2. Relationship between a Cylinder and a Cone:

- A cylinder is a three-dimensional shape with two congruent circular bases and a curved surface.

- The volume of a cylinder (V) is given by the formula: V = πr²h, where r is the radius of the base and h is the height.

- A cone is a three-dimensional shape with a circular base and a curved surface tapering to a point (apex).

- The volume of a cone (V) is calculated using the formula: V = (1/3) × πr²h.

- When comparing the volumes of a cylinder and a cone:

  - If they have the same base radius and height, the cylinder will have three times the volume of the cone.

  - This is because the cylinder fills up space more efficiently due to its shape.

 

3. Relationship between a Cylinder and a Sphere:

- A cylinder is a three-dimensional shape with two congruent circular bases and a curved surface.

- The volume of a cylinder (V) is given by the formula: V = πr²h, where r is the radius of the base and h is the height.

- A sphere is a three-dimensional shape with all points equidistant from a central point, forming a perfectly round shape.

- The volume of a sphere (V) is calculated using the formula: V = (4/3) × πr³, where r is the radius.

- When comparing the volumes of a cylinder and a sphere:

  - If they have the same radius, the sphere will have a greater volume than the cylinder.

  - This is because a sphere has more volume packed within its shape compared to a cylinder of the same radius. 


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