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3D Cross Sections

Grade 6 · Geometry · Worksheet 1

  1. Noah is designing a cylindrical grain silo for his family's farm. The silo has a diameter of 8 meters and a height of 12 meters. If Noah makes a horizontal cut parallel to the circular base at a height of 5 meters from the bottom, what is the area of the circular cross-section he would see? Use π = 3.14 and round your answer to the nearest hundredth.
    Answer: ______________
  2. Maria is designing a cylindrical water tank for her school's science project. The tank has a diameter of 1.8 meters and a height of 2.5 meters. If she makes a horizontal cut parallel to the base at a height of 1.2 meters from the bottom, what is the area of the circular cross-section she would see? Use π = 3.14 and round your answer to the nearest hundredth.
    Answer: ______________
  3. Maria is designing a triangular prism-shaped container for her art supplies. The triangular base has a height of 8 cm and a base length of 6 cm, and the prism has a length of 15 cm. If Maria makes a vertical cut parallel to the triangular ends, what is the area of the triangular cross-section she creates? Answer: ______________
  4. Mere slices a rectangular prism that is 1200 cm long, 800 cm wide, and 600 cm high with a horizontal cut one-third of the way up from the base. What is the area of the cross section in square centimeters? Answer: ______________
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Answer Key & Explanations

3D Cross Sections · Grade 6 · Worksheet 1

  1. Noah is designing a cylindrical grain silo for his family's farm. The silo has a diameter of 8 meters and a height of 12 meters. If Noah makes a horizontal cut parallel to the circular base at a height of 5 meters from the bottom, what is the area of the circular cross-section he would see? Use π = 3.14 and round your answer to the nearest hundredth. Answer: 50.24 Solution: Identify the diameter of the cylinder, which is 8 meters. Calculate the radius by dividing the diameter by 2. Radius = 8 / 2 = 4 meters.
    Full step-by-step solution

    Step 1: Identify the diameter of the cylinder, which is 8 meters. Step 2: Calculate the radius by dividing the diameter by 2. Radius = 8 / 2 = 4 meters. Step 3: Use the formula for the area of a circle: Area = π × radius². Step 4: Substitute the values: Area = 3.14 × (4)² = 3.14 × 16. Step 5: Calculate the product: 3.14 × 16 = 50.24. Step 6: The area is already to the nearest hundredth. The area of the circular cross-section is 50.24 square meters.

  2. Maria is designing a cylindrical water tank for her school's science project. The tank has a diameter of 1.8 meters and a height of 2.5 meters. If she makes a horizontal cut parallel to the base at a height of 1.2 meters from the bottom, what is the area of the circular cross-section she would see? Use π = 3.14 and round your answer to the nearest hundredth. Answer: 2.54 Solution: Identify that a horizontal cut through a cylinder creates a circular cross-section. The diameter of this circle is the same as the diameter of the cylinder, which is 1.8 meters.
    Full step-by-step solution

    Step 1: Identify that a horizontal cut through a cylinder creates a circular cross-section. Step 2: The diameter of this circle is the same as the diameter of the cylinder, which is 1.8 meters. Step 3: Calculate the radius of the circle: radius = diameter ÷ 2 = 1.8 ÷ 2 = 0.9 meters. Step 4: Calculate the area of the circular cross-section using the formula: area = π × radius². Step 5: Substitute the values: area = 3.14 × (0.9)² = 3.14 × 0.81 = 2.5434 square meters. Step 6: Round to the nearest hundredth: 2.54 square meters. The area of the circular cross-section is 2.54 square meters.

  3. Maria is designing a triangular prism-shaped container for her art supplies. The triangular base has a height of 8 cm and a base length of 6 cm, and the prism has a length of 15 cm. If Maria makes a vertical cut parallel to the triangular ends, what is the area of the triangular cross-section she creates? Answer: 24 Solution: When cutting parallel to the triangular ends of a triangular prism, the cross-section is a triangle identical to the base triangle. The base triangle has a height of 8 cm and a base length of 6 cm.
    Full step-by-step solution

    Step 1: When cutting parallel to the triangular ends of a triangular prism, the cross-section is a triangle identical to the base triangle. Step 2: The base triangle has a height of 8 cm and a base length of 6 cm. Step 3: The area of a triangle is calculated as (base × height) ÷ 2. Step 4: Area = (6 cm × 8 cm) ÷ 2 = 48 cm² ÷ 2 = 24 cm². The area of the triangular cross-section is 24 square centimeters.

  4. Mere slices a rectangular prism that is 1200 cm long, 800 cm wide, and 600 cm high with a horizontal cut one-third of the way up from the base. What is the area of the cross section in square centimeters? Answer: 960000 Solution: A horizontal cut through a rectangular prism creates a cross section that is a rectangle parallel to the base. The length is 1200 cm and the width is 800 cm.
    Full step-by-step solution

    Step 1: A horizontal cut through a rectangular prism creates a cross section that is a rectangle parallel to the base. Step 2: The cross section has the same length and width as the base of the prism, regardless of the height of the cut. Step 3: The length is 1200 cm and the width is 800 cm. Step 4: Area of a rectangle = length × width. Step 5: Area = 1200 × 800 = 960000 square cm. The answer is 960000 square cm.