Let A ⊂ R 3 be Jordan-measurable in R 3 . Define the function a: R → [0, ∞) by a(h) = λ 2 ({(x, y) ∈ R 2 | (x, y, h) ∈ A}), that is, the area of {(x, y) ∈ R 2 | (x, y, h) ∈ A}, for all h ∈ R. 1. Justify that a is well-defined. 2. Let h1 = inf{h ∈ R | a(h) > 0} and h2 = sup{h ∈ R | a(h) > 0}. Show that if the restriction of a to [h1, h2] is a polynomial of degree at most 3, then the volume of A is given by λ 3 (A) = h2 − h1 6 a(h1) + a(h2) + 4a h1 + h2 2 . 3. Using the above formula, find the volume of a cone of height H > 0 and base area B > 0.