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#1: What is the volume of a Prism?

#2: What is the volume of a Pyramid?

#3: What is the difference of a Prism and a Pyramid?

#4: What is the difference of finding the Volume and finding the Surface Area?

1 answer

#1: What is the volume of a Prism?

The volume \( V \) of a prism can be calculated using the formula:

\[ V = B \cdot h \]

where \( B \) is the area of the base of the prism, and \( h \) is the height (the perpendicular distance between the two bases).

#2: What is the volume of a Pyramid?

The volume \( V \) of a pyramid can be calculated using the formula:

\[ V = \frac{1}{3} B \cdot h \]

where \( B \) is the area of the base of the pyramid, and \( h \) is the height (the perpendicular distance from the base to the apex).

#3: What is the difference between a Prism and a Pyramid?

The main differences between a prism and a pyramid are:

  1. Shape: A prism has two congruent bases that are connected by rectangular faces, while a pyramid has one base and triangular faces that converge at a single apex.
  2. Volume Calculation: The volume of a prism is found using the area of the base multiplied by the height, whereas the volume of a pyramid is one-third of the base area multiplied by the height.
  3. Faces: A prism has two bases and additional lateral faces, while a pyramid has one base and triangular faces that are angles leading up to the apex.

#4: What is the difference between finding the Volume and finding the Surface Area?

The main differences between finding volume and surface area are:

  1. Definition:

    • Volume measures the amount of space inside a three-dimensional shape and is expressed in cubic units.
    • Surface Area measures the total area of the outer surfaces of a three-dimensional shape and is expressed in square units.

  2. Purpose:

    • Volume is important for understanding capacity, such as how much fluid a container can hold.
    • Surface area is important for applications involving coating, painting, or material usage since it represents the area covering the object.

  3. Calculation:

    • The calculation of volume typically involves multiplying dimensions (like height, base area) and may involve specific geometric formulas.
    • Surface area calculations may involve adding the area of all faces of a shape together and can also use geometric formulas specific to the shape.