Section 1 - Surface area and volume of prisms. Flashcards
What is a prism?
A prism is a three-dimensional shape with two parallel, congruent bases connected by rectangular faces.
True or False: The bases of a prism can be of different shapes.
False
Fill in the blank: The surface area of a prism is calculated by adding the areas of the ______ and the lateral surface area.
bases
What formula is used to calculate the volume of a prism?
Volume = Base Area × Height
What is the surface area of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm?
Surface Area = 2lw + 2lh + 2wh = 2(53) + 2(54) + 2(3*4) = 30 + 40 + 24 = 94 cm²
True or False: The volume of a prism is measured in cubic units.
True
What do you call the two identical faces of a prism?
Bases
What is the lateral surface area of a prism?
The lateral surface area is the sum of the areas of all the side faces of the prism.
How do you find the base area of a triangular prism with a base of 6 cm and height of 4 cm?
Base Area = (1/2) × base × height = (1/2) × 6 × 4 = 12 cm²
Multiple Choice: Which of the following is NOT a type of prism? A) Rectangular prism B) Triangular prism C) Circular prism D) Hexagonal prism
C) Circular prism
True or False: The height of a prism is the perpendicular distance between the two bases.
True
What is the formula for the lateral surface area of a rectangular prism?
Lateral Surface Area = 2h(l + w)
If a cylinder is considered a prism, what are its bases?
The two circular bases
Calculate the volume of a triangular prism with a base area of 10 cm² and a height of 5 cm.
Volume = Base Area × Height = 10 × 5 = 50 cm³
Fill in the blank: The total surface area of a prism is the sum of its lateral surface area and the area of ______.
the bases
What is the surface area of a cube with side length 3 cm?
Surface Area = 6s² = 6(3)² = 54 cm²
What is the volume of a cube with a side length of 4 cm?
Volume = s³ = 4³ = 64 cm³
True or False: The surface area of a prism can be expressed in square units.
True
What is the relationship between the area of the base and the volume of the prism?
The volume is directly proportional to the base area multiplied by the height.
Fill in the blank: The dimensions of a prism are typically measured in ______.
units
How do you calculate the surface area of a pentagonal prism?
Surface Area = (Perimeter of base × Height) + (2 × Area of base)
What is the formula for calculating the volume of a cylinder?
Volume = πr²h
What does ‘h’ represent in the volume formula of a prism?
The height of the prism
Calculate the lateral surface area of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.
Lateral Surface Area = 2h(l + w) = 2(5)(4 + 3) = 70 cm²
True or False: All prisms have identical bases.
True
What is the effect of doubling the height of a prism on its volume?
The volume will also double.
Multiple Choice: Which formula would you use to find the volume of a prism? A) Area × Base B) Base Area × Height C) Height × Width D) Length × Width
B) Base Area × Height
Fill in the blank: The surface area of a prism is measured in ______.
square units
What is the total surface area of a prism with a base area of 20 cm² and a height of 10 cm?
Total Surface Area = Lateral Surface Area + 2 × Base Area
