Volume Worksheets - Free Printable
Educational worksheet: Volume Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Volume Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Volume Worksheets
- First, look closely: The image displays a math worksheet titled "Volume of Prisms and Cylinders." It contains nine diagrams of 3D shapes (labeled A through I) with some dimensions provided. The task is to calculate the volume for each shape and round the answer to two decimal places, using 3.14 for π. The shapes include cylinders, triangular prisms, rectangular prisms, and trapezoidal prisms. To solve this, I need to identify the correct volume formula for each shape type and apply it using the given measurements.
- Next, find information: I will need to recall or verify the standard volume formulas for these geometric solids.
- Volume of a Cylinder: V = π * r² * h
- Volume of a Prism: V = Base Area * Height
- For a Triangular Prism: Base Area = (1/2) * base * height of triangle
- For a Rectangular Prism: Base Area = length * width
- For a Trapezoidal Prism: Base Area = (1/2) * (sum of parallel sides) * height of trapezoid
- Then, review the findings: The formulas are standard and do not require external research. I can proceed to calculate the volume for each shape based on its diagram and given dimensions.
I will now calculate the volume for each shape one by one.
Shape A (Cylinder):
- Radius (r) = 5 units
- Height (h) = 8 units
- Volume = π * r² * h = 3.14 * 5² * 8 = 3.14 * 25 * 8 = 628.00 cubic units
Shape B (Triangular Prism):
- Base of triangle = 7 units
- Height of triangle = 6 units
- Length of prism = 10 units
- Base Area = (1/2) * 7 * 6 = 21 square units
- Volume = 21 * 10 = 210.00 cubic units
Shape C (Rectangular Prism):
- Length = 12 units
- Width = 5 units
- Height = 8 units
- Volume = 12 * 5 * 8 = 480.00 cubic units
Shape D (Trapezoidal Prism):
- Parallel sides of trapezoid = 8 units and 12 units
- Height of trapezoid = 6 units
- Length of prism = 10 units
- Base Area = (1/2) * (8 + 12) * 6 = (1/2) * 20 * 6 = 60 square units
- Volume = 60 * 10 = 600.00 cubic units
Shape E (Triangular Prism):
- Base of triangle = 8 units
- Height of triangle = 6 units
- Length of prism = 9 units
- Base Area = (1/2) * 8 * 6 = 24 square units
- Volume = 24 * 9 = 216.00 cubic units
Shape F (Rectangular Prism):
- Length = 6 units
- Width = 4 units
- Height = 10 units
- Volume = 6 * 4 * 10 = 240.00 cubic units
Shape G (Cylinder):
- Diameter = 10 units, so Radius (r) = 5 units
- Height (h) = 12 units
- Volume = π * r² * h = 3.14 * 5² * 12 = 3.14 * 25 * 12 = 942.00 cubic units
Shape H (Cylinder):
- Radius (r) = 6 units
- Height (h) = 10 units
- Volume = π * r² * h = 3.14 * 6² * 10 = 3.14 * 36 * 10 = 1130.40 cubic units
Shape I (Trapezoidal Prism):
- Parallel sides of trapezoid = 6 units and 10 units
- Height of trapezoid = 5 units
- Length of prism = 8 units
- Base Area = (1/2) * (6 + 10) * 5 = (1/2) * 16 * 5 = 40 square units
- Volume = 40 * 8 = 320.00 cubic units
A: 628.00
B: 210.00
C: 480.00
D: 600.00
E: 216.00
F: 240.00
G: 942.00
H: 1130.40
I: 320.00
- Next, find information: I will need to recall or verify the standard volume formulas for these geometric solids.
- Volume of a Cylinder: V = π * r² * h
- Volume of a Prism: V = Base Area * Height
- For a Triangular Prism: Base Area = (1/2) * base * height of triangle
- For a Rectangular Prism: Base Area = length * width
- For a Trapezoidal Prism: Base Area = (1/2) * (sum of parallel sides) * height of trapezoid
- Then, review the findings: The formulas are standard and do not require external research. I can proceed to calculate the volume for each shape based on its diagram and given dimensions.
I will now calculate the volume for each shape one by one.
Shape A (Cylinder):
- Radius (r) = 5 units
- Height (h) = 8 units
- Volume = π * r² * h = 3.14 * 5² * 8 = 3.14 * 25 * 8 = 628.00 cubic units
Shape B (Triangular Prism):
- Base of triangle = 7 units
- Height of triangle = 6 units
- Length of prism = 10 units
- Base Area = (1/2) * 7 * 6 = 21 square units
- Volume = 21 * 10 = 210.00 cubic units
Shape C (Rectangular Prism):
- Length = 12 units
- Width = 5 units
- Height = 8 units
- Volume = 12 * 5 * 8 = 480.00 cubic units
Shape D (Trapezoidal Prism):
- Parallel sides of trapezoid = 8 units and 12 units
- Height of trapezoid = 6 units
- Length of prism = 10 units
- Base Area = (1/2) * (8 + 12) * 6 = (1/2) * 20 * 6 = 60 square units
- Volume = 60 * 10 = 600.00 cubic units
Shape E (Triangular Prism):
- Base of triangle = 8 units
- Height of triangle = 6 units
- Length of prism = 9 units
- Base Area = (1/2) * 8 * 6 = 24 square units
- Volume = 24 * 9 = 216.00 cubic units
Shape F (Rectangular Prism):
- Length = 6 units
- Width = 4 units
- Height = 10 units
- Volume = 6 * 4 * 10 = 240.00 cubic units
Shape G (Cylinder):
- Diameter = 10 units, so Radius (r) = 5 units
- Height (h) = 12 units
- Volume = π * r² * h = 3.14 * 5² * 12 = 3.14 * 25 * 12 = 942.00 cubic units
Shape H (Cylinder):
- Radius (r) = 6 units
- Height (h) = 10 units
- Volume = π * r² * h = 3.14 * 6² * 10 = 3.14 * 36 * 10 = 1130.40 cubic units
Shape I (Trapezoidal Prism):
- Parallel sides of trapezoid = 6 units and 10 units
- Height of trapezoid = 5 units
- Length of prism = 8 units
- Base Area = (1/2) * (6 + 10) * 5 = (1/2) * 16 * 5 = 40 square units
- Volume = 40 * 8 = 320.00 cubic units
A: 628.00
B: 210.00
C: 480.00
D: 600.00
E: 216.00
F: 240.00
G: 942.00
H: 1130.40
I: 320.00
Parent Tip: Review the logic above to help your child master the concept of volume of shapes worksheet.
