3D Shapes - Volume Formulas Quiz

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<p>v = 1/3 × π × r² × h (B)</p> Signup and view all the answers

<p>v = 4/3 × π × r³ (C)</p> Signup and view all the answers

Volume equals length times width times height (v = l × w × h).

Volume equals one third times length times width times height (v = 1/3 × l × w × h).

Volume equals pi times radius squared times height (v = π × r² × h).

Volume equals one third times pi times radius squared times height (v = 1/3 × π × r² × h).

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Volume equals four thirds times pi times radius cubed (v = 4/3 × π × r³).

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Prism: Volume calculated by multiplying length (l), width (w), and height (h). Formula: v = l × w × h, commonly used for rectangular prisms but applicable to any prism type.
Pyramid: Volume is one-third of the base area multiplied by height. Formula: v = 1/3 × l × w × h, showing how pyramids compress space as height increases relative to base.
Cylinder: Volume determined by the area of the circular base multiplied by the height. Formula: v = π × r² × h, where r is the radius, emphasizing the importance of circular geometry.
Cone: Similar to pyramids, their volume equals one-third of the base area times height. Formula: v = 1/3 × π × r² × h, highlighting the relationship between conic sections and circles.
Sphere: Volume representation of a perfectly round object. Formula: v = 4/3 × π × r³, illustrating how volume expands cubically with radius, demonstrating key spherical properties.