Final answer:
The base area of a cylinder with a volume of 150 cubic cm and a height of 10 cm can be calculated by rearranging the formula V = πr²h, leading to the answer of 15π square cm.
Step-by-step explanation:
To find the base area of a cylinder with a given volume and height, we can rearrange the formula for the volume of a cylinder, which is V = πr²h. For a cylinder with a volume of 150 cubic cm and a height of 10 cm, the formula becomes 150 cm³ = πr² × 10 cm. Dividing both sides by 10 cm and π gives us the radius squared, r².
By rearranging the equation, we get r² = ⅔ cm². To calculate the base area A, which is πr², we use A = π × (⅔ cm²), resulting in A being 15π square cm.
Therefore, the correct answer is (d) 15π square cm.