Henry has a fenced yard in the shape of a rectangle with a perimeter that measures 242 feet. If the width of the yard measures 5
1 answer:
Answer: Length = 70 feet
Concept:
Here, we need to know how to find the perimeter of a rectangle.
Perimeter (rectangle) = 2 (l + w)
l = length
w = width
Solve:
<u>Given information</u>
l = l
w = 51 feet
P = 242 feet
<u>Given expression</u>
P = 2 (l + w)
<u>Substitute values into the expression</u>
242 = 2 (l + 51)
<u>Divide 2 on both sides</u>
242 / 2 = 2 (l + 51) / 2
121 = l + 51
<u>Subtract 51 on both sides</u>
121 - 51 = l + 51 - 51
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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:
