3D Cross Sections

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Answer Key & Explanations

3D Cross Sections · Grade 6 · Worksheet 2

1. A rectangular prism-shaped shipping container has dimensions of 15 meters by 8 meters by 6 meters. If you make a horizontal cut parallel to the base at a height of 4 meters from the bottom, what is the area of the rectangular cross-section created by this cut? Answer: 120 Solution: When making a horizontal cut parallel to the base, the cross-section will have the same length and width as the base of the prism. The base dimensions are 15 meters by 8 meters.
   Full step-by-step solution

   Step 1: When making a horizontal cut parallel to the base, the cross-section will have the same length and width as the base of the prism. Step 2: The base dimensions are 15 meters by 8 meters. Step 3: The area of a rectangle is calculated by multiplying length times width. Step 4: Area = 15 × 8 = 120 square meters. Step 5: The height of the cut (4 meters) doesn't affect the area of the cross-section since all horizontal cross-sections parallel to the base have the same dimensions. The answer is 120.

2. Emma slices a rectangular prism that has a length of 20 cm, a width of 15 cm, and a height of 10 cm. She makes a horizontal cut halfway up the height. What is the area of the resulting cross section in square centimeters? Answer: 300 Solution: A horizontal cut through a rectangular prism creates a rectangle that is parallel to the base. Step 2: The cross section will have the same length and width as the base of the prism.
   Full step-by-step solution

   Step 1: A horizontal cut through a rectangular prism creates a rectangle that is parallel to the base. Step 2: The cross section will have the same length and width as the base of the prism. Step 3: The length is 20 cm and the width is 15 cm. Step 4: The area of a rectangle is length times width. Step 5: Area = 20 cm × 15 cm = 300 square cm. The answer is 300.

3. Noah is designing a new community center shaped like a rectangular prism. The building will be 48 meters long, 32 meters wide, and 24 meters tall. If the architect draws a horizontal cross-section of the building at a height of 18 meters above the ground, what will be the area of this cross-section in square meters? Answer: 1536 Solution: A horizontal cross-section of a rectangular prism is always a rectangle with the same length and width as the base. The length of the cross-section is 48 meters. The width of the cross-section is 32 meters.
   Full step-by-step solution

   Step 1: A horizontal cross-section of a rectangular prism is always a rectangle with the same length and width as the base. Step 2: The length of the cross-section is 48 meters. Step 3: The width of the cross-section is 32 meters. Step 4: Calculate the area: Area = length × width = 48 × 32 Step 5: 48 × 30 = 1440 Step 6: 48 × 2 = 96 Step 7: 1440 + 96 = 1536 Step 8: The area of the cross-section is 1536 square meters.

4. Mere slices a cube with a side length of 14 cm with a horizontal cut halfway up its height. What is the area of the cross section? Answer: 196 square cm Solution: A horizontal cut through a cube creates a square cross section parallel to the base. The cross section has the same side length as the cube, which is 14 cm. Area of a square = side × side.
   Full step-by-step solution

   Step 1: A horizontal cut through a cube creates a square cross section parallel to the base. Step 2: The cross section has the same side length as the cube, which is 14 cm. Step 3: Area of a square = side × side. Step 4: Area = 14 × 14 = 196 square cm. The answer is 196 square cm.

5. Emma is designing a new skateboard ramp shaped like a triangular prism. The ramp has a triangular base with a height of 1.2 meters and base length of 2.5 meters, and the prism extends 4 meters in length. If Emma makes a vertical cut perpendicular to the triangular face, creating a cross-section parallel to the rectangular sides, what is the area of this rectangular cross-section in square meters? Answer: 4.8 Solution: Identify the dimensions of the rectangular cross-section. The prism length is given as 4 meters.
   Full step-by-step solution

   Step 1: Identify the dimensions of the rectangular cross-section. When cutting vertically perpendicular to the triangular face, the cross-section will be a rectangle with one dimension equal to the prism's length and the other dimension equal to the height of the triangular base. Step 2: The prism length is given as 4 meters. Step 3: The height of the triangular base is given as 1.2 meters. Step 4: Calculate the area of the rectangle: Area = length × height = 4 × 1.2 Step 5: 4 × 1.2 = 4.8 The area of the rectangular cross-section is 4.8 square meters.