Which expression gives the height of a cylinder in terms of its volume and base area?

Which expression gives the height of a cylinder in terms of its volume and base area?

• A. height = volume - base area
• B. height = base area / volume
• C. height = volume * base area
• D. height = volume / base area

Answer: (D)

Think in terms of how volume, base area, and height are related for a cylinder. The volume comes from stacking the base area up through the height, so V = base_area × height. To get the height alone, you solve for h by dividing both sides by the base area: h = volume ÷ base_area. This is the expression that uses the given volume and base area to find the height. The other forms don’t match this relationship. Subtracting base area from volume mixes units in a way that wouldn’t yield a length, multiplying volume by base area gives an oversized quantity with wrong units, and dividing base_area by volume yields an inverse unit that isn’t a height. So the correct expression is volume divided by base area.

Think in terms of how volume, base area, and height are related for a cylinder. The volume comes from stacking the base area up through the height, so V = base_area × height. To get the height alone, you solve for h by dividing both sides by the base area: h = volume ÷ base_area. This is the expression that uses the given volume and base area to find the height.

The other forms don’t match this relationship. Subtracting base area from volume mixes units in a way that wouldn’t yield a length, multiplying volume by base area gives an oversized quantity with wrong units, and dividing base_area by volume yields an inverse unit that isn’t a height. So the correct expression is volume divided by base area.