Question

what is the formula for the volume of a cylinder with r = o?
v = \\(\frac{4}{3}\pi o^3\\)
v = \\(\frac{1}{3}\pi o^2 h\\)
v = \\(\pi o^2 h\\)
v = \\(2\pi o h + 2b\\)
v = \\(\pi o l + b\\)

Explanation:

Step1: Recall Cylinder Volume Formula

The volume of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Here, \( r = o \), so substitute \( r \) with \( o \).

Step2: Match with Options

• Option 1: \( V = \frac{4}{3}\pi o^3 \) is the volume of a sphere. Eliminate.
• Option 2: \( V = \frac{1}{3}\pi o^2 h \) is the volume of a cone. Eliminate.
• Option 3: \( V = \pi o^2 h \) matches the cylinder volume formula (with \( r = o \)).
• Option 4: \( V = 2\pi o h + 2B \) is the surface area of a cylinder (lateral + 2 bases). Eliminate.
• Option 5: \( V = \pi o l + B \) is the surface area of a cone (lateral + base). Eliminate.

Answer:

C. \( V = \pi o^2 h \) (Note: Assuming the third option is labeled as C; if original labels were A - E, adjust accordingly. Based on the options, the correct one is the third option with \( V = \pi o^2 h \))