An apple pie 10 cm in diameter costs $1.50. Then, an apple pie 20 cm in diameter should cost
a. $3.00
b. $4.00
c. $4.50
d. $6.00
e. $8.00
please answer and explain
To find the cost of an apple pie with a 20 cm diameter, we can use the concept of area.
The formula to find the area of a circle is:
Area = π * (radius)^2
To compare the two apple pies, we need to find out how the area is related to the diameters. The radius is equal to half of the diameter, so if the diameter doubles, the radius also doubles.
For the first apple pie with a diameter of 10 cm, the radius would be 10/2 = 5 cm.
To find the area of the first apple pie, we use the formula:
Area = π * (5 cm)^2 = 25π cm^2
Now, for the second apple pie with a diameter of 20 cm, the radius would be 20/2 = 10 cm.
To find the area of the second apple pie, we use the formula:
Area = π * (10 cm)^2 = 100π cm^2
Now, let's compare the two areas. The area of the second apple pie is 100π cm^2, which is four times larger than the area of the first apple pie (25π cm^2).
Since the cost of the first apple pie is $1.50, we need to multiply that by four to find the cost of the second apple pie:
$1.50 * 4 = $6.00
Therefore, an apple pie with a 20 cm diameter should cost $6.00. So, the correct answer is option d. $6.00.
Those are awfully small apple pies.
Area = pi * r^2
A = 3.14 * 5^2
A = 78.5 square cm.
1.5 / 78.5 = $0.019 per square cm
A = 3.14 * 10^2
A = 314 sq. cm
314 * 0.019 = $5.97
Since cost usually varies with the area
and the area is proportional to the square of the corresponding sides, the area would be 4 times as large, thus the cost would be 4($1.5) or $6.00
( ratio of sides = 2:1
so ratio of areas = 2^2 : 1^2 = 4 : 1
ratio of costs = 4 : 1 )