Answer:
5/8 = 0.625 and 62.5%
11/12 = 0.917 and 91.67%
1/4 = 0.25 and 25%
3/5 = 0.6 and 60%
Step-by-step explanation:
:)
The two parabolas intersect for

and so the base of each solid is the set

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas,
. But since -2 ≤ x ≤ 2, this reduces to
.
a. Square cross sections will contribute a volume of

where ∆x is the thickness of the section. Then the volume would be

where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

We end up with the same integral as before except for the leading constant:

Using the result of part (a), the volume is

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

and using the result of part (a) again, the volume is

8, the answer needs to be more than a certain amount of characters.
<h3>
Answer:</h3>
c) 7π cm
<h3>
Step-by-step explanation:</h3>
The length of an arc (s) is related to its central angle (θ) and the radius of the circle (r) by ...
... s = rθ . . . . . . . . . θ in radians
Here, the central angle measures are given in "grads". There are 400 grads in a circle, so 200 grads in π radians. To convert grads to radians, we multiply the number of grads by π/(200g).
Then the lengths of the arcs are ...
... arc AB = (20 cm)·(50g·(π/(200g))) = 5π cm
... arc BC = (10 cm)·(40g·(π/(200g))) = 2π cm
E = arc AB + arc BC = 5π cm + 2π cm = 7π cm