Final answer:
The volume of the second cylinder is found using the equation V = 7/8(x cm³) + 8 cm³, which simplifies to solving for x in 7x = 8(224 cm³), resulting in a second cylinder volume of 256 cm³. The correct equation is V = 7/8(216 cm³ + 8 cm³).
Step-by-step explanation:
Given that one cylinder's volume is 8 cm³ less than 7/8 of the volume of a second cylinder and the first cylinder's volume is 216 cm³, we can set up an equation to find the volume of the second cylinder. Since 7/8 of the second cylinder's volume is 8 cm³ more than the first cylinder's volume, we can express it as V = 7/8(x cm³) + 8 cm³, where V is the volume of the first cylinder (216 cm³). Equating and simplifying, we have 216 cm³ = 7/8(x cm³) - 8 cm³. Cross multiplying both sides to clear the fraction, we get 7x = 8(216 cm³ + 8 cm³), which simplifies to 7x = 8(224 cm³).
Dividing both sides by 7 to isolate x gives us x = (8/7) × 224 cm³, which simplifies to x = 256 cm³. Thus, the second cylinder's volume is 256 cm³. The correct equation representing the volume of the second cylinder is therefore option B: V = 7/8(216 cm³ + 8 cm³).