To complete your activity on calculating the volume and surface area of 3-D objects, here's how you could structure your work based on the guidelines provided. Below is an example using a rectangular prism (a box) and a cylinder (a can).
Example Table of Work
| Prism/Pyramid (Rectangular Prism) | Cone/Cylinder (Cylinder) | |-------------------------------------|--------------------------| | Measurements: | Measurements: | | Length: 10 cm | Diameter: 6 cm | | Width: 5 cm | Radius: 3 cm | | Height: 8 cm | Height: 10 cm | | Base Area Calculation: | Base Area Calculation:| | Area = Length × Width | Area = π × r² | | Area = 10 cm × 5 cm = 50 cm² | Area = 3.14 × (3 cm)² | | | Area = 3.14 × 9 cm² | | | Area = 28.26 cm² | | | | | Volume Calculation: | Volume Calculation: | | Volume = Base Area × Height | Volume = Base Area × Height| | Volume = 50 cm² × 8 cm | Volume = 28.26 cm² × 10 cm| | Volume = 400 cm³ | Volume = 282.6 cm³ | | | | | Surface Area Calculation: | Surface Area Calculation: | | SA = 2lw + 2lh + 2wh | SA = 2πrh + 2πr² | | SA = 2(10 cm)(5 cm) + 2(10 cm)(8 cm) + 2(5 cm)(8 cm)| SA = 2(3.14)(3 cm)(10 cm) + 2(3.14)(3 cm)²| | SA = 100 cm² + 160 cm² + 80 cm² | SA = 188.4 cm² + 56.52 cm² | | SA = 340 cm² | SA = 244.92 cm² |
Total Measurements and Calculations:
- Rectangular Prism:
- Base Area: 50 cm²
- Volume: 400 cm³
- Surface Area: 340 cm²
- Cylinder:
- Base Area: 28.26 cm²
- Volume: 282.6 cm³
- Surface Area: 244.92 cm²
Reflection Questions
Question 1: The units for base area calculations should be in square centimeters (cm²) because area is a two-dimensional measurement expressed in square units. In contrast, volume calculations are in cubic centimeters (cm³) because volume is a three-dimensional measurement that accounts for length, width, and height, thus requiring cubic units.
Question 2: If you were to take a cross-section parallel to the base of the rectangular prism, you would see a rectangle with the same dimensions as the base (10 cm x 5 cm). A cross-section cannot be a sphere because a sphere is a three-dimensional shape, and its cross-section will always result in a circle, not a complete sphere. A cross-section represents a two-dimensional slice of a three-dimensional object.
Once you complete your table and reflections, you can submit them as required. Make sure that your measurements and calculations are accurate and clearly presented.