Select the appropriate shape for the given volume formula.

Question

v = pi r squared h.

v = four-thirds pi r cubed.

v = l w h.

v = one-third pi r squared.

Answer 1

The volume formulas provided correspond to different shapes:

1. v = πr²h: This formula represents the volume of a cylinder. Here, \( r \) is the radius of the base, and \( h \) is the height of the cylinder.

2. v = (4/3)πr³: This formula represents the volume of a sphere. Here, \( r \) is the radius of the sphere.

3. v = lwh: This formula represents the volume of a rectangular prism (or cuboid), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

4. v = (1/3)πr²h: This formula represents the volume of a cone. Here, \( r \) is the radius of the base, and \( h \) is the height of the cone.

In summary:

• Cylinder: \( v = πr²h \)
• Sphere: \( v = (4/3)πr³ \)
• Rectangular Prism: \( v = lwh \)
• Cone: \( v = (1/3)πr²h \)