For a cylinder with volume V and base area B, which expression gives the height?

• A. Height = Base Area / Volume
• B. Height = Volume / Base Area
• C. Height = Volume × Base Area
• D. Height = Volume − Base Area

Answer: (B)

This question tests how a cylinder’s volume relates to its base area and its height. The volume of a cylinder is the base area times the height: V = B × h. To find the height, solve for h by dividing both sides by the base area: h = V / B. So the height is Volume divided by Base Area. This makes sense dimensionally too: base area has units of length^2 and volume has length^3, so V/B has units of length, which is what height should be.

The other forms don’t fit because they’d produce incorrect units or combine quantities in ways that don’t match how volume is defined. For instance, dividing the base area into the volume gives units of 1/length, multiplying volume and base area gives an inappropriate, overly large unit, and subtracting them mixes incompatible units.

For a quick check, if the volume is 314 cm^3 and the base area is 98.7 cm^2, the height would be 314 / 98.7 ≈ 3.18 cm.