Answer:
Amount of empty space in the cylinder = 395.64 cm³
Step-by-step explanation:
Since the cylinder contains 3 tennis balls each measuring 6 cm in diameter, we can say that the diameter of the cylinder is 6 cm because the balls are on top of each other. Since we have 18 cm is the height of the cylinder,then;
Formula for volume of a cylinder is;
V = πr²h
We are to use π = 3.14
Thus, V_cylinder = 3.14 × (6/2)² × 18
V_cylinder = 508.68 cm³
Volume of a tennis ball is;
V_tennis ball = (4/3)πr³
V_tennis ball = (4/3) × 3.14 × (6/2)³
V_tennis ball = 37.68 cm³
Thus, volume of 3 tennis balls = 3 × 37.68 = 113.04 cm³
Amount of empty space in the cylinder = V_cylinder - V_3 tennnis ball = 508.68 - 113.04 = 395.64 cm³
Since
, and you have a corresponding term in the given Riemann sum of
, you know the integral is being taken over an interval of length 5, so you can omit the second choice.
Next,
corresponds to
with
. The fact that
alone tells you that the interval of integration starts at 3, and since we know the interval has length 5, that leaves the first choice as the correct answer.
Answer: List of the angles from smallest to largest are C, B and A
Step-by-step explanation:
The diagram of triangle ABC is shown in the attached photo. Since none of the sides are equal, then it is a scalene triangle.
From the information given,
AB = m – 2
BC = m + 4
AC = m
It means that the longest side is BC, the medium side is AC and the shortest side is AB. Therefore,
The smallest angle is angle C.
The medium angle is angle B.
The largest angle is angle A
The answer is: "12 feet" .
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Note: In a square, the length of EACH of the four sides of the square is the same.
Area = Length * width.
For a square, length = width.
So for a square, Area = length * width = (length of a side)² = s² ,
Given: A = s² = 144 ft² ;
Solve for the positive value of "s" .
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→ s² = 144 ft² ; Take the "square root" of each side ;
→ √(s²) = √(144 ft²) ;
→ s = 12 ft.
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The answer is: 12 ft.
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