Question

Brian is transferring cake batter from a 10 × 14 in rectangular pan to a 10 in diameter round pan. Write a function that calculates the height of the batter in the round pan as a function of the height of the batter in the rectangular pan. If the height of the batter in the rectangular pan is 2 in, will it fit in such a round pan with 3 in sides?

a) The function is h(r) = (7/5) × r. No, the batter will not fit in the round pan with 3 in sides.
b) The function is h(r) = (5/7) × r. Yes, the batter will fit in the round pan with 3 in sides.
c) The function is h(r) = (3/5) × r. No, the batter will not fit in the round pan with 3 in sides.
d) The function is h(r) = (5/3) × r. Yes, the batter will fit in the round pan with 3 in sides.

Answer 1

Option D). To calculate the height of the batter in the round pan, we can use the concept of volume. The correct function to calculate the height of the batter as a function of the height in the rectangular pan is (5/3) × r. If the height of the batter in the rectangular pan is 2 in, it will fit in the round pan with 3 in sides.

Step-by-step explanation:

To calculate the height of the batter in the round pan, we can use the concept of volume. The volume of the batter in the rectangular pan is equal to length times width times height. So, for the rectangular pan with dimensions 10 × 14 and a height of 2, the volume is: 10 × 14 × 2 = 280.

The volume of the round pan can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height. We can rearrange the formula to solve for h: h = V / (πr²).

Given that the diameter of the round pan is 10 inches, the radius is 5 inches. Substituting the values, we get: h = 280 / (π × 5²) = 280 / 78.54 ≈ 3.56 inches.

Since the height of the batter in the rectangular pan is 2 inches, it will fit in the round pan with 3.56 inches of height. Therefore, the correct answer is d) The function is h(r) = (5/3) × r. Yes, the batter will fit in the round pan with 3 in sides.