Final answer:
To calculate the area of a circle with a diameter 1.5 times larger than another circle, you increase the radius proportionally and apply the area formula A = πr², resulting in the new area being 2.25 times the original area.
Step-by-step explanation:
The area of a circle is given by the formula A = πr², where r is the radius of the circle. To find the area of a circle with a diameter that is 1.5 times the diameter of the first circle, we need to compare the radii of the two circles. Since the diameter is twice the radius, if the diameter is 1.5 times larger, the radius will also be 1.5 times larger.
The area of the second circle will be A' = π(1.5r)². Expanding this, we get A' = π(1.5²)(r²) = π(2.25)r². The new area is 2.25 times the area of the original circle. Since the original area is 96 square inches, the new area will be 96 inches² × 2.25 = 216 square inches.