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3D Volume Formulas

Grade 8 · Geometry · Worksheet 2

  1. Hana is designing a set of decorative containers for a community art project. She has a cylindrical container with a radius of 8 inches and a height of 18 inches. She also has a cone-shaped container with the same radius of 8 inches and a height of 18 inches. Hana wants to fill both containers completely with colored sand. How much more sand, in cubic inches, will the cylinder hold than the cone? Use π ≈ 3.14 and round your answer to the nearest whole cubic inch.
    Answer: ______________
  2. A spherical water tank has a radius of 9 feet. What is its volume in cubic feet? (Use π = 3.14) Answer: ______________
  3. Noah is designing a large decorative planter for a community garden. The planter is shaped like a cylinder with a radius of 9 inches and a height of 24 inches. Inside the planter, there is a conical insert (open at the top) that sits upside down, with its tip at the bottom of the cylinder, to hold a small tree. The cone has the same radius as the cylinder (9 inches) and a height of 12 inches. Noah needs to fill the remaining space around the cone with soil. What is the volume of soil needed, in cubic inches? Use π ≈ 3.14 and round your answer to the nearest whole cubic inch.
    Answer: ______________
  4. A sphere has a radius of 9 cm. What is its volume? (Use π = 3.14) Answer: ______________
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Answer Key & Explanations

3D Volume Formulas · Grade 8 · Worksheet 2

  1. Hana is designing a set of decorative containers for a community art project. She has a cylindrical container with a radius of 8 inches and a height of 18 inches. She also has a cone-shaped container with the same radius of 8 inches and a height of 18 inches. Hana wants to fill both containers completely with colored sand. How much more sand, in cubic inches, will the cylinder hold than the cone? Use π ≈ 3.14 and round your answer to the nearest whole cubic inch. Answer: 2412 Solution: Find the volume of the cylinder. V_cylinder = π × r² × h = 3.14 × 8² × 18 = 3.14 × 64 × 18 = 3.14 × 1152 = 3617.28 cubic inches. Find the volume of the cone.
    Full step-by-step solution

    Step 1: Find the volume of the cylinder. V_cylinder = π × r² × h = 3.14 × 8² × 18 = 3.14 × 64 × 18 = 3.14 × 1152 = 3617.28 cubic inches. Step 2: Find the volume of the cone. V_cone = (1/3) × π × r² × h = (1/3) × 3.14 × 8² × 18 = (1/3) × 3.14 × 64 × 18 = (1/3) × 3.14 × 1152 = (1/3) × 3617.28 = 1205.76 cubic inches. Step 3: Find the difference. Difference = V_cylinder - V_cone = 3617.28 - 1205.76 = 2411.52 cubic inches. Rounded to the nearest whole cubic inch: 2412 cubic inches. The answer is 2412.

  2. A spherical water tank has a radius of 9 feet. What is its volume in cubic feet? (Use π = 3.14) Answer: 3052.08 Solution: Use the formula for the volume of a sphere: V = (4/3)πr³ Substitute the given radius: r = 9 feet, π = 3.14 Calculate r³: 9³ = 9 × 9 × 9 = 81 × 9 = 729 Multiply by π: 729 × 3.14 = 2289.06 Multiply by 4/3: (4/3) × 2289.06 = (4 × 2289.06) ÷ 3 = 9156.24 ÷ 3 = 3052.08 The volume of the spherical…
    Full step-by-step solution

    Step 1: Use the formula for the volume of a sphere: V = (4/3)πr³ Step 2: Substitute the given radius: r = 9 feet, π = 3.14 Step 3: Calculate r³: 9³ = 9 × 9 × 9 = 81 × 9 = 729 Step 4: Multiply by π: 729 × 3.14 = 2289.06 Step 5: Multiply by 4/3: (4/3) × 2289.06 = (4 × 2289.06) ÷ 3 = 9156.24 ÷ 3 = 3052.08 The volume of the spherical water tank is 3052.08 cubic feet.

  3. Noah is designing a large decorative planter for a community garden. The planter is shaped like a cylinder with a radius of 9 inches and a height of 24 inches. Inside the planter, there is a conical insert (open at the top) that sits upside down, with its tip at the bottom of the cylinder, to hold a small tree. The cone has the same radius as the cylinder (9 inches) and a height of 12 inches. Noah needs to fill the remaining space around the cone with soil. What is the volume of soil needed, in cubic inches? Use π ≈ 3.14 and round your answer to the nearest whole cubic inch. Answer: 5087 Solution: Find the volume of the cylindrical planter. Formula: V_cylinder = π × r² × h V_cylinder = 3.14 × 9² × 24 V_cylinder = 3.14 × 81 × 24 V_cylinder = 3.14 × 1944 V_cylinder = 6104.16 cubic inches Find the volume of the conical insert.
    Full step-by-step solution

    Step 1: Find the volume of the cylindrical planter. Formula: V_cylinder = π × r² × h V_cylinder = 3.14 × 9² × 24 V_cylinder = 3.14 × 81 × 24 V_cylinder = 3.14 × 1944 V_cylinder = 6104.16 cubic inches Step 2: Find the volume of the conical insert. Formula: V_cone = (1/3) × π × r² × h V_cone = (1/3) × 3.14 × 9² × 12 V_cone = (1/3) × 3.14 × 81 × 12 V_cone = (1/3) × 3.14 × 972 V_cone = (1/3) × 3052.08 V_cone = 1017.36 cubic inches Step 3: Subtract the cone's volume from the cylinder's volume to find the soil volume. Soil volume = 6104.16 - 1017.36 Soil volume = 5086.80 cubic inches Rounded to the nearest whole cubic inch: 5087 cubic inches. The answer is 5087.

  4. A sphere has a radius of 9 cm. What is its volume? (Use π = 3.14) Answer: 3052.08 cm³ Solution: Write the formula for the volume of a sphere: V = 4/3 × π × r³ Substitute the given radius (r = 9 cm) and π = 3.14: V = 4/3 × 3.14 × 9³ Calculate the cube of the radius: 9³ = 9 × 9 × 9 = 729 Multiply by π: 3.14 × 729 = 2289.06 Multiply by 4/3: 2289.06 × 4/3 = 2289.06 × 4 ÷ 3 = 9156.24 ÷ 3 =…
    Full step-by-step solution

    Step 1: Write the formula for the volume of a sphere: V = 4/3 × π × r³ Step 2: Substitute the given radius (r = 9 cm) and π = 3.14: V = 4/3 × 3.14 × 9³ Step 3: Calculate the cube of the radius: 9³ = 9 × 9 × 9 = 729 Step 4: Multiply by π: 3.14 × 729 = 2289.06 Step 5: Multiply by 4/3: 2289.06 × 4/3 = 2289.06 × 4 ÷ 3 = 9156.24 ÷ 3 = 3052.08 The volume of the sphere is 3052.08 cm³.