1. What is the formula for the surface area of a right rectangular prism?
The formula for the surface area of a right rectangular prism is:
SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
2. What is the formula for the volume of a right rectangular prism?
The formula for the volume of a right rectangular prism is:
V = lwh, where l, w, and h represent the length, width, and height of the prism.
3. A right rectangular prism has a length of 8 cm, a width of 3 cm, and a height of 5 cm. Find its surface area and volume.
Using the formulas mentioned earlier:
SA = 2(8)(3) + 2(8)(5) + 2(3)(5) = 94 cm^2
V = (8)(3)(5) = 120 cm^3
Therefore, the surface area of the rectangular prism is 94 cm^2 and the volume is 120 cm^3.
4. What is a pyramid?
A pyramid is a polyhedron with a polygonal base and triangular faces that converge to a single point called the vertex.
5. What is the formula for the surface area of a pyramid?
The formula for the surface area of a pyramid is:
SA = (1/2)pl + B, where p represents the perimeter of the base, l represents the slant height, and B represents the area of the base.
6. What is the formula for the volume of a pyramid?
The formula for the volume of a pyramid is:
V = (1/3)Bh, where B represents the area of the base and h represents the height of the pyramid.
7. A triangle pyramid has a base with sides measuring 6 cm, 8 cm, and 10 cm. The slant height is 7 cm. Find its surface area and volume.
Using the formulas mentioned earlier:
p = 6 + 8 + 10 = 24 cm
B = (1/2)(6)(8) = 24 cm^2
SA = (1/2)(24)(7) + 24 = 108 cm^2
V = (1/3)(24)(h) = 8h cm^3 (where h represents the height)
Therefore, the surface area of the pyramid is 108 cm^2 and the volume is 8h cm^3.
8. What is the main difference between a prism and a pyramid?
The main difference between a prism and a pyramid is that a prism has two congruent polygonal bases with parallelogram faces, while a pyramid has one polygonal base and triangular faces that converge to a point at the top.
9. True or False: All right rectangular prisms have rectangular bases.
True. The base of a right rectangular prism is always a rectangle.
10. True or False: A pyramid can have a triangular base.
True. A pyramid can have bases of any polygon shape, including triangles.
Right Rectangular Prisms & Pyramids final exam
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