[Q3] FINDING THE VOLUMES OF SOLIDS

 [Q3] FINDING THE VOLUMES OF SOLIDS

Volume of Different Solids

By: PJ MIANA

 

1. Cube:

   - Definition: A cube is a three-dimensional shape with six square faces of equal size.  All angles are right angles, and all edges have the same length.

   - Formula: Volume = Side³  or V=s3

   - Sample Computation:

     - If the side length is 5 meters.

     - Volume = 5m x 5m x 5m

     - Volume = 125 cubic meters



 2. Rectangular Prism:

   - Definition: A rectangular prism is a three-dimensional shape with six faces, each of which is a rectangle. Opposite faces are equal and parallel to each other.

   - Formula: Volume = Length x Width x Height or V = lwh

   - Sample Computation:

     - If the length is 8 meters, width is 4 meters, and height is 3 meters.

     - Volume = 8m x 4m x 3m

     - Volume = 96 cubic meters

3. Pyramid:

   - Definition: A pyramid is a three-dimensional shape with a polygonal base and triangular faces that meet at a common point called the apex.

   - Formula: Volume = (1/3) × Base Area × Height or V=1/3 Bh

   - Sample Computation:

     - If the base area is 36 square meters and the height is 12 meters.

     - Volume = (1/3) × 36m² × 12m

     - Volume = 144 cubic meters



 

4. Cylinder:

   - Definition: A cylinder is a three-dimensional shape with two circular bases of equal size connected by a curved surface.

   - Formula: Volume = πr²h

   - Sample Computation:

     - If the radius of the base is 5 meters and the height is 10 meters.

     - Volume = π(5m)²(10m)

     - Volume ≈ 785.4 cubic meters

 

5. Cone:

   - Definition: A cone is a three-dimensional shape with a circular base and a curved surface that tapers to a point called the apex.

   - Formula: Volume = (1/3) × πr² × Height or V = (1/3) πr²H

   - Sample Computation:

     - If the radius of the base is 6 meters and the height is 8 meters.

     - Volume = (1/3) × π(6m)² × 8m

     - Volume ≈ 301.6 cubic meters

 

6. Sphere:

   - Definition: A sphere is a perfectly round three-dimensional object in which every point on the surface is equidistant from the center.

   - Formula: Volume = (4/3)πr³ or V=(4/3)πr³

   - Sample Computation:

     - If the radius of the sphere is 7 meters.

     - Volume = (4/3)π(7m)³

     - Volume ≈ 1436.8 cubic meters



Understanding the formulas and computations for finding the volume of different solids helps us solve various problems in mathematics, engineering, and everyday life.




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