Answer:
about 10.24 ft
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . where h is the height and r is the radius
The formula for the volume of a sphere is ...
V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r
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We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.
Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...
22,500 ft³ = πr²·(20/3)r = (20π/3)r³
Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...
r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft
The radius of the silo should be about 10.24 feet.
Answer:
x = 7
Step-by-step explanation:
A triangle's total interior angle measurement will equal 180°.
Set all measurements equal to 180:
(82) + (9x - 6) + (6x - 1) = 180
Simplify. Combine like terms:
(82 - 6 - 1) + (9x + 6x) = 180
(82 - 7) + (15x) = 180
(75) + 15x = 180
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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First, Subtract 75 from both sides of the equation:
15x + 75 = 180
15x + 75 (-75) = 180 (-75)
15x = 180 - 75
15x = 105
Next, divide 15 from both sides of the equation:
(15x)/15 = (105)/15
x = 105/15
x = 7
7 is your value for x.
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Answer:
4
Step-by-step explanation:
60 minutes = 1 hour → 120 minutes = 2 hours. The purple bar represents at least 121 minutes, which is greater than 2 hours.
