Right Rectangular Prisms & Pyramids Sample Work
Sample Work:
1. Find the volume of a right rectangular prism with dimensions length = 6 cm, width = 4 cm, and height = 5 cm.
Solution:
The volume of a right rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Substituting the given values, we have V = 6 cm * 4 cm * 5 cm = 120 cm³.
Therefore, the volume of the right rectangular prism is 120 cm³.
2. Find the surface area of a right rectangular prism with dimensions length = 10 cm, width = 7 cm, and height = 3 cm.
Solution:
The surface area of a right rectangular prism is given by the formula A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Substituting the given values, we have A = 2 * 10 cm * 7 cm + 2 * 10 cm * 3 cm + 2 * 7 cm * 3 cm = 140 cm² + 60 cm² + 42 cm² = 242 cm².
Therefore, the surface area of the right rectangular prism is 242 cm².
3. Find the volume of a pyramid with base dimensions length = 8 cm, width = 6 cm, and height = 9 cm.
Solution:
The volume of a pyramid is given by the formula V = (1/3) * base area * height, where base area is the product of the base dimensions and height is the height of the pyramid.
Substituting the given values, we have V = (1/3) * (8 cm * 6 cm) * 9 cm = (1/3) * 48 cm² * 9 cm = 144 cm³.
Therefore, the volume of the pyramid is 144 cm³.
4. Find the surface area of a pyramid with base dimensions length = 12 cm, width = 10 cm, and height = 6 cm.
Solution:
The surface area of a pyramid is given by the formula A = base area + (1/2) * perimeter of base * slant height, where base area is the product of the base dimensions and the perimeter of base is the sum of all the sides of the base.
First, we need to find the slant height using the Pythagorean theorem:
slant height = √(height² + ((length/2)²)) = √(6 cm)² + (6 cm)² = √36 cm² + 36 cm² = √72 cm² = 6√2 cm.
Substituting the given values, we have A = (12 cm * 10 cm) + (1/2) * (12 cm + 10 cm + 10 cm + 12 cm) * 6√2 cm = 120 cm² + 44 cm * 6√2 cm = 120 cm² + 264√2 cm² ≈ 625.9 cm².
Therefore, the surface area of the pyramid is approximately 625.9 cm².