The values for h(r) are found by dividing the volume V(r) by the base area B(r) for each given radius of the cylinder. Following this method, the heights for each radius, 2, 8, 10, and 12 cm, are 4 cm, 16 cm, 20 cm, and 24 cm, respectively.
The values that complete the table for h(r) can be found by rearranging the formula for the volume of a cylinder, V = πr²h, and solving for h. The base area B(r) is given by πr² which is equivalent to the expressions given in the table for B(r) with respect to r. To find h(r), we need to divide the volume V(r) by the area B(r).
For example, when r = 2, we have B(r) = 4π cm² and V(r) = 16 cm³. Applying the formula h(r) = V(r) / B(r), we get h(r) = 16 cm³ / (4π cm²) = 4 cm. By applying this method to each radius value, we can find the corresponding heights.
For r = 8, B(r) = 64 cm² and V(r) = 1,024 cm³, so h(r) = 1,024 / 64 = 16 cm.
For r = 10, B(r) = 100 cm² and V(r) = 2,000 cm³, so h(r) = 2,000 / 100 = 20 cm.
For r = 12, B(r) = 144 cm² and V(r) = 3,456 cm³, so h(r) = 3,456 / 144 = 24 cm.
Therefore, the complete table for h(r) in centimeters is 4, 16, 20, and 24 for the given radii 2, 8, 10, and 12 cm, respectively.
The probable question may be:
Given a set of functions h(r), B(r), and V(r) modeling the relationship between the height, base area, and volume of cylinders respectively in relation to their radii, and provided with specific radius values of 2, 8, 10, and 12, could you determine and elaborate on how these functions correspond to the measured values of height, base area, and volume for each cylinder?