Volume Concepts

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Answer Key & Explanations

Volume Concepts · Grade 5 · Worksheet 1

1. Maria is building a rectangular planter box for her garden. The box measures 1.5 meters in length, 0.8 meters in width, and 0.6 meters in height. If she wants to fill it with soil, how many cubic meters of soil will she 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 volume of a rectangular box is found by multiplying its length, width, and height. Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters Write the formula for the volume of a rectangular box.
   Full step-by-step solution

   To find the amount of soil needed to fill the planter box, we need to calculate its volume. The volume of a rectangular box is found by multiplying its length, width, and height. Step 1: Write down the given dimensions. Length = 1.5 meters Width = 0.8 meters Height = 0.6 meters Step 2: Write the formula for the volume of a rectangular box. Volume = Length × Width × Height Step 3: Substitute the given numbers into the formula. Volume = 1.5 × 0.8 × 0.6 Step 4: Perform the multiplication step by step. First, multiply the first two numbers. 1.5 × 0.8 = 1.20 Step 5: Now multiply the result by the third number. 1.20 × 0.6 = 0.720 Step 6: Since the problem asks for the answer in cubic meters, and our calculation is already in meters, we have our final volume. We can write 0.720 as 0.72. Therefore, Maria will need 0.72 cubic meters of soil to completely fill the planter box.

2. Emma is designing a fish tank for her classroom. The tank is shaped like a rectangular prism and measures 1.2 meters in length, 0.75 meters in width, and 0.9 meters in height. If she fills the tank completely with water, what is the volume of water in cubic meters? Answer: 0.81 Solution: Identify the dimensions: length = 1.2 m, width = 0.75 m, height = 0.9 m Use the volume formula for a rectangular prism: Volume = length × width × height Multiply the numbers: 1.2 × 0.75 = 0.9 Multiply the result by the height: 0.9 × 0.9 = 0.81 The volume is 0.81 cubic meters
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.2 m, width = 0.75 m, height = 0.9 m Step 2: Use the volume formula for a rectangular prism: Volume = length × width × height Step 3: Multiply the numbers: 1.2 × 0.75 = 0.9 Step 4: Multiply the result by the height: 0.9 × 0.9 = 0.81 Step 5: The volume is 0.81 cubic meters

3. ∛1728 = ? Answer: 12 Solution: We need to find the cube root of 1728, which means finding a number that when multiplied by itself three times equals 1728.
   Full step-by-step solution

   Step 1: We need to find the cube root of 1728, which means finding a number that when multiplied by itself three times equals 1728. Step 2: Try 10: 10 × 10 × 10 = 1000 (too small) Step 3: Try 12: 12 × 12 × 12 = 144 × 12 = 1728 Step 4: Since 12 × 12 × 12 = 1728, the cube root of 1728 is 12. The answer is 12.

4. 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.

5. 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.

6. Isabella is packing a moving box shaped like a rectangular prism. The box has a length of 18 inches, a width of 12 inches, and a height of 15 inches. How many cubic inches of space are inside the box? Answer: 3240 Solution: The volume of a rectangular prism is found by multiplying length × width × height. Substitute the given dimensions: 18 × 12 × 15. First multiply length and width: 18 × 12 = 216.
   Full step-by-step solution

   Step 1: The volume of a rectangular prism is found by multiplying length × width × height. Step 2: Substitute the given dimensions: 18 × 12 × 15. Step 3: First multiply length and width: 18 × 12 = 216. This is the number of cubes in the bottom layer. Step 4: Multiply by the height: 216 × 15 = 3240. Step 5: The volume is 3240 cubic inches. The answer is 3240.