Prisms

Show your work for each problem.

1.
What shape are the lateral faces (sides) of any prism?
1. a)Triangles
2. b)Pentagons
3. c)Circles
4. d)Rectangles
Answer: Rectangles
The lateral faces of any prism are always rectangles. They connect the two parallel bases, no matter what shape the bases are.
2.
A prism has hexagonal bases. What is it called?
1. a)Triangular prism
2. b)Rectangular prism
3. c)Pentagonal prism
4. d)Hexagonal prism
Answer: Hexagonal prism
Since the bases are hexagons, it's called a hexagonal prism. Prisms are always named after the shape of their bases.
3.
A rectangular prism has length 6 cm, width 4 cm, and height 3 cm. What is its volume in cm³?
Answer: 72
cm³. For a rectangular prism, multiply all three dimensions together.
4.
A cube has sides of 5 cm. What is its volume in cm³?
Answer: 125
cm³. A cube is a special rectangular prism where all edges are equal.
5.
Which formula is correct for calculating the volume of ANY prism?
1. a)
2. b)
3. c)
4. d)
Answer:
works for any prism. is for pyramids, is surface area, and is for cylinders.
6.
A triangular prism has a triangular base with base 8 cm and height 5 cm. The prism is 12 cm long. What is the volume in cm³?
Answer: 240
Base area = cm². Volume = cm³.
7.
Find the surface area of a rectangular prism with length 8 cm, width 5 cm, and height 3 cm.
Answer: 158
1. Calculate the area of the top/bottom faces (2 × length × width) 80
2. Calculate the area of the front/back faces (2 × length × height) 48
3. Calculate the area of the side faces (2 × width × height) 30
4. Add all three results to get the total surface area 158
8.
A rectangular box holds 180 cm³ of water. If the base is 6 cm by 5 cm, what is the height of the box in cm?
Answer: 6
Base area = cm². Height = Volume ÷ Base area = cm.
9.
A triangular prism has a right-angled triangular base with legs 6 cm and 8 cm (hypotenuse 10 cm). The prism is 15 cm long. Find the surface area.
Answer: 408
1. Find the area of ONE triangular base (½ × 6 × 8) 24
2. Find the area of BOTH bases (multiply by 2) 48
3. Find the perimeter of the triangular base (6 + 8 + 10) 24
4. Find the lateral surface area (perimeter × height) 360
5. Add the base areas and lateral area for total surface area 408
10.
Which of these is NOT a prism?
1. a)Rectangular prism
2. b)Triangular prism
3. c)Cube
4. d)Cylinder
Answer: Cylinder
A cylinder has circular bases, not polygon bases. Prisms must have polygon bases (triangles, rectangles, etc.).
11.
An aquarium is 50 cm long, 30 cm wide, and 40 cm tall. How many liters of water can it hold? (1 liter = 1000 cm³)
Answer: 60
1. Calculate the volume in cm³ (50 × 30 × 40) 60000
2. Convert to liters by dividing by 1000 60
12.
A tent has a triangular cross-section with base 3 m and height 2 m. The tent is 4 m long. What is the volume of air inside in m³?
Answer: 12
Base area = m². Volume = m³.
13.
A gift box is 20 cm × 15 cm × 10 cm. How much wrapping paper (in cm²) is needed to cover all sides?
Answer: 1300
1. Calculate top/bottom faces: 2 × (20 × 15) 600
2. Calculate front/back faces: 2 × (20 × 10) 400
3. Calculate left/right faces: 2 × (15 × 10) 300
4. Add all areas for total surface area 1300
14.
Two prisms have the same base area of 25 cm². One is 8 cm tall and the other is 12 cm tall. What is the difference in their volumes in cm³?
Answer: 100
Volume 1 = cm³. Volume 2 = cm³. Difference = cm³.
15.
A triangular prism has a base with sides 5 cm, 12 cm, and 13 cm (a right triangle). The prism is 20 cm long. Find its volume.
Answer: 600
1. For a right triangle, which sides are the legs (perpendicular)? 5 and 12
2. Calculate the area of the triangular base: ½ × 5 × 12 30
3. Multiply the base area by the prism length to find volume 600