(a) To find the base area of the larger jar, we can use the concept of geometric similarity. Since the two jars are geometrically similar, their corresponding sides are proportional. The ratio of their heights is 12 cm / 8 cm = 3/2.
Since the ratio of their heights is 3/2, the ratio of their base areas will be (3/2)^2 = 9/4.
Given that the base area of the smaller jar is 42 cm^2, we can find the base area of the larger jar by multiplying 42 cm^2 by the ratio of their base areas:
Base area of larger jar = 42 cm^2 * (9/4) = 94.5 cm^2.
Therefore, the base area of the larger jar is 94.5 cm^2.
(b) If the cost of the larger jar of jam is $5, we can assume that the cost is directly proportional to the base area of the jar.
Since the base area of the larger jar is 94.5 cm^2, and the cost is $5, we can set up a proportion to find the cost of the smaller jar:
Cost of smaller jar / Cost of larger jar = Base area of smaller jar / Base area of larger jar.
Let's call the cost of the smaller jar "x":
x / $5 = 42 cm^2 / 94.5 cm^2.
We can solve for "x" by cross-multiplying and then dividing:
x = ($5 * 42 cm^2) / 94.5 cm^2.
Calculating this, we find that the cost of the smaller jar of jam is approximately $2.23.
Therefore, the cost of the smaller jar of jam is $2.23.