Volume Concepts

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Volume Concepts · Grade 5 · Worksheet 3

1. Liam is building a rectangular planter box for his garden. The box measures 1.5 meters in length, 0.8 meters in width, and 0.6 meters in height. He needs to fill it with soil to grow vegetables. How many cubic meters of soil does Liam need to completely fill the planter box? Answer: 0.72 Solution: To find the amount of soil needed to fill the planter box, we need to calculate its volume. The box is a rectangular prism, so the formula for volume is: Volume = Length × Width × Height Write down the given measurements.
   Full step-by-step solution

   To find the amount of soil needed to fill the planter box, we need to calculate its volume. The box is a rectangular prism, so the formula for volume is: Volume = Length × Width × Height Step 1: Write down the given measurements. Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters Step 2: Multiply the length and width. 1.5 × 0.8 = 1.2 Step 3: Multiply the result by the height. 1.2 × 0.6 = 0.72 Step 4: Interpret the result. The volume is 0.72 cubic meters. Therefore, Liam needs 0.72 cubic meters of soil to fill the planter box completely.

2. Kaia is helping her school's art club build a giant rectangular planter for the school garden. The planter needs to be 12 meters long, 9 meters wide, and 2 meters deep. They will fill it completely with soil. What is the volume of the planter in cubic meters? Answer: 216 Solution: The planter is a rectangular prism. Volume = length × width × height. Step 2: Length = 12 m, width = 9 m, height (depth) = 2 m.
   Full step-by-step solution

   Step 1: The planter is a rectangular prism. Volume = length × width × height. Step 2: Length = 12 m, width = 9 m, height (depth) = 2 m. Step 3: Multiply 12 × 9 = 108. Step 4: Multiply 108 × 2 = 216. The volume is 216 cubic meters.

3. Emma is designing a fish tank for her classroom. The tank is shaped like a rectangular prism and measures 1.2 meters long, 0.75 meters wide, and 0.9 meters high. How many cubic meters of water will the tank hold when completely filled? Answer: 0.81 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 1.2 × 0.75 × 0.9 Multiply length and width first: 1.2 × 0.75 = 0.9 Multiply the result by height: 0.9 × 0.9 = 0.81 The volume is 0.81 cubic meters The answer is 0.81.
   Full step-by-step solution

   Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given measurements: Volume = 1.2 × 0.75 × 0.9 Step 3: Multiply length and width first: 1.2 × 0.75 = 0.9 Step 4: Multiply the result by height: 0.9 × 0.9 = 0.81 Step 5: The volume is 0.81 cubic meters The answer is 0.81.

4. Liam is building a rectangular planter box for his garden. The box measures 1.5 meters long, 0.8 meters wide, and 0.6 meters high. If he fills the box completely with soil, how many cubic meters of soil will he need? Answer: 0.72 Solution: To find the amount of soil needed, we need to calculate the volume of the rectangular planter box. The formula for the volume of a rectangular box is: Volume = length × width × height Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters 1.5 × 0.8 = 1.2 1.2 × 0.6 = 0.72 Volume = 0.72 cubic…
   Full step-by-step solution

   To find the amount of soil needed, we need to calculate the volume of the rectangular planter box. The formula for the volume of a rectangular box is: Volume = length × width × height Step 1: Write down the given dimensions: Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters Step 2: Multiply the length and width first: 1.5 × 0.8 = 1.2 Step 3: Multiply the result by the height: 1.2 × 0.6 = 0.72 Step 4: Include the unit for volume: Volume = 0.72 cubic meters So, Liam will need 0.72 cubic meters of soil to fill the box completely.

5. A rectangular prism is drawn with length 12 cm, width 8 cm, and height 5 cm. What is the volume of this prism? Answer: 480 Solution: The formula for volume of a rectangular prism is length × width × height Multiply the length and width to find the area of the base: 12 cm × 8 cm = 96 square cm Multiply the base area by the height to find the volume: 96 square cm × 5 cm = 480 cubic cm The volume is 480 cubic centimeters The…
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Multiply the length and width to find the area of the base: 12 cm × 8 cm = 96 square cm Step 3: Multiply the base area by the height to find the volume: 96 square cm × 5 cm = 480 cubic cm Step 4: The volume is 480 cubic centimeters The answer is 480.

6. Noah is building a rectangular fish tank for his classroom. The tank measures 120 cm in length, 60 cm in width, and 50 cm in height. How many liters of water does Noah need to completely fill the fish tank? (Remember: 1 liter = 1000 cubic centimeters) Answer: 360 Solution: Volume = length × width × height Volume = 120 cm × 60 cm × 50 cm 120 × 60 = 7,200 7,200 × 50 = 360,000 So volume = 360,000 cubic centimeters Since 1 liter = 1,000 cubic centimeters 360,000 ÷ 1,000 = 360 Noah needs 360 liters of water to fill the fish tank completely.
   Full step-by-step solution

   Step 1: Calculate the volume in cubic centimeters Volume = length × width × height Volume = 120 cm × 60 cm × 50 cm Step 2: Multiply the dimensions 120 × 60 = 7,200 7,200 × 50 = 360,000 So volume = 360,000 cubic centimeters Step 3: Convert cubic centimeters to liters Since 1 liter = 1,000 cubic centimeters 360,000 ÷ 1,000 = 360 Step 4: Final answer Noah needs 360 liters of water to fill the fish tank completely.

7. ∛216 = ? Answer: 6 Solution: We are asked to find the cube root of 216: ∛216. The cube root of a number x is the number y such that y × y × y = x. Try small integers to see if 216 is a perfect cube.
   Full step-by-step solution

   We are asked to find the cube root of 216: ∛216. Step 1: Understand the cube root. The cube root of a number x is the number y such that y × y × y = x. Step 2: Try small integers to see if 216 is a perfect cube. Let's test 5: 5 × 5 × 5 = 125. That’s too small. Let's test 6: 6 × 6 × 6 = 36 × 6 = 216. Step 3: Check the result. 6 × 6 = 36. 36 × 6 = 216. Yes, that matches exactly. Step 4: Conclusion. Since 6 cubed equals 216, the cube root of 216 is 6. Final answer: 6