Final answer:
To make the base area of Padima's igloo 4 times larger than Jamilla's, Padima needed to double the radius from 2 feet to 4 feet. Due to the area formula A = πr², doubling the radius of a circle results in quadrupling the area, which satisfies Padima's requirement.
Step-by-step explanation:
To determine which change in dimension Padima had to make to ensure his igloo's base area was exactly 4 times larger than Jamilla's, we need to recall the formula for the area of a circle, which is A = πr². Given that Jamilla has constructed a round igloo with a radius of 2 feet, the area of her igloo's base would be π(2²) = 4π square feet. If Padima wants his igloo's base to have an area 4 times larger, we would need an area of 4 × (4π) = 16π square feet.
To find the necessary radius for Padima's igloo, we set up the equation: 16π = πr². Dividing both sides by π, we get ²16 = r². Taking the square root of both sides gives us r = 4 feet. Thus, Padima needed to double the radius of her igloo from 2 feet to 4 feet to make the base area 4 times larger.
Option a) is correct because doubling the radius of a circle results in a new area which is four times the original area because the area of a circle is proportional to the square of the radius. Doubling the radius (2r) and squaring it gives (2r)² = 4r², showing that the area is four times larger.