Answer:
3.1%
Step-by-step explanation:
6/196 × 100% = 3.1%
Answer:
Step-by-step explanation:
<u>Sides of the picture added margin:</u>
<u>Solution</u>:
- A(margin) = Total area - A(picture)
- (8 + 2x)(5 + 2x) - 5*8 = 30
- 4x² + 10x + 16x + 40 - 40 - 30 = 0
- 4x² + 26x - 30 = 0
- 2x² + 13x - 15 = 0
- x = (-13 + √(13² + 2*4*15))/4
- x = (-13 + 17)/4
- x = 1 cm
Note. The other root is ignored as negative.
(a) First find the intersections of

and

:

So the area of

is given by

If you're not familiar with the error function

, then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.
(b) Find the intersections of the line

with

.

So the area of

is given by


which is approximately 1.546.
(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve

and the line

, or

. The area of any such circle is

times the square of its radius. Since the curve intersects the axis of revolution at

and

, the volume would be given by
The volume of air needed is equal to the volume of the sphere, which is 7,234.56 cm^3.
<h3>
How to get the volume of a sphere?</h3>
The volume of air that we need is equal to the volume of the basketball.
Remember that for a sphere of radius R, the volume is:
V = (4/3)*3.14*R^3
In this case, the radius is 12cm, replacing that we get:
V = (4/3)*3.14*(12cm)^3 = 7,234.56 cm^3
Then, to fully inflate the ball, we need 7,234.56 cm^3 of air.
If you want to learn more about spheres, you can read:
brainly.com/question/10171109