Geometry
Volume
Volume measures the space inside a 3D shape. Key formulas: Rectangular prism = lwh, Cylinder = πr²h, Cone = ⅓πr²h, Sphere = (4/3)πr³.
Watch & Learn
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Find the volume of a cylinder with radius 4 and height 10
Step-by-Step Solution
V = πr²h
V = π(4)²(10) = π(16)(10) = 160π ≈ 502.65 cubic units
Answer
V = 160π ≈ 502.65 cubic units
Problem
Find the volume of a cone with radius 3 and height 9
Step-by-Step Solution
V = ⅓πr²h
V = ⅓π(3)²(9) = ⅓π(9)(9) = 27π ≈ 84.82 cubic units
Answer
V = 27π ≈ 84.82 cubic units
Problem
Find the volume of a rectangular prism: 5 × 4 × 3
Step-by-Step Solution
V = l × w × h
V = 5 × 4 × 3 = 60
Answer
V = 60 cubic units
Problem
Find the volume of a sphere with radius 6
Step-by-Step Solution
V = (4/3)πr³
V = (4/3)π(6)³ = (4/3)π(216) = 288π ≈ 904.78 cubic units
Answer
V = 288π ≈ 904.78 cubic units
Problem
A cylinder has volume 200π and height 8. Find the radius.
Step-by-Step Solution
V = πr²h → 200π = πr²(8)
r² = 200/8 = 25
r = 5
Answer
Radius = 5 units
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Volume of rectangular prism: 6 × 4 × 5?
Volume of cylinder: radius 3, height 7?
Volume of cone: radius 6, height 4?
Volume of sphere: radius 3?
Volume of cube with side 5?
Volume of cylinder: radius 5, height 10?
Volume of cone: radius 3, height 9?
Volume of rectangular prism: 10 × 2 × 3?
Volume of sphere: radius 1?
A cylinder has radius 4 and height 5. What is its volume?
Volume of cube with side 10?
A cone has radius 6 and height 10. What is its volume?
Finished all 12? Give yourself a pat on the back — then check your work!
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