Answer:
sqrt(146)
Step-by-step explanation:
The distance between these two points can be the hypotenuse of our right triangle.
We can create a right triangle with two legs of length 11 and 5. To solve for the hypotenuse, we apply the pythagorean theorem
sqrt(5^2+11^2)=sqrt(146)
I attached a graph to help you visualize the triangle and how it works.
If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.
So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.
This means that the perimeter is
feet long. But we know that this is 510 feet, so we have
.
So, the three sides are 110, 160 and 240 feet long.
To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if is half the perimeter of the triangle whose sides are
, the area
is given by
In our case, so the formula becomes
Answer:
The volume of the ball with the drilled hole is:
Step-by-step explanation:
See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:
Then we set the integral for the volume by using shell method:
That can be solved by substitution:
The limits of integration also change:
For x=5:
For x=15:
So the integral becomes:
If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:
Then applying the basic rule we get:
Since that is just half of the solid, we multiply by 2 to get the complete volume:
