Final answer:
To find the depth of water in a rectangular container transferred from a cylindrical container, we calculate the volume of the cylinder and set it equal to the volume of the rectangular prism. After calculating and substituting π with 'p', the depth comes out to approximately 24 cm, which leads us to the closest option, which is E: 25 cm.
Step-by-step explanation:
The question requires us to calculate the depth of water when transferred from a cylindrical container to a rectangular one while keeping the volume of water constant. To do so, we need to know the volume of water in the cylindrical container first. The volume (πr2h) of the cylinder can be calculated using its height (28 cm) and diameter (18 cm; radius is 9 cm). Once we have the volume of the cylindrical container, we can calculate the depth of the water in the rectangular container using the volume formula for a rectangular prism (lwh) where l, w, and h represent the length, width, and height(depth) respectively.
In this case, the volume of the cylinder is: V = π(9 cm)2(28 cm) = 2,268π cm3
The volume of the rectangular container must equal the volume of the cylindrical container. So:
2,268π cm3 = 27 cm * 11 cm * h
Solving for h, we get: h = 2,268π / (27 * 11) cm = 2,268π / 297 cm = 7.64π cm.
Since we are using π as "p", we replace π with p to get: h = 7.64p cm. And as we use the approximate value of π (pi) which is 3.14 we get h ≈ 24 cm. However, as the options are in integers, we have to choose the closest value which is Option E: 25 cm.