Answer:
The area is 21.
Step-by-step explanation:
Let

be the solid. Then the volume is

which follows from the facts that

(by computing the Jacobian)
and

(we take the positive solution, since it's clear that

lies above the

-

plane)

(again, taking the positive root for the same reason)





Answer:
244 cm³
Step-by-step explanation:
Step 1: Given data
Height of the prism with a pentagonal base (h): 8 cm
Area of the pentagonal base (A): 30.5 cm²
Step 2: Calculate the volume of the prism with a pentagonal base
We have a regular pentagonal prism, that is, the 5 sides of the base are equal and we know the area of the base and the height of the prism. We can calculate its volume using the following expression.
V = A × h
V = 30.5 cm² × 8 cm = 244 cm³