A barrel in the shape of a cylinder has a height of 4.5 feet and a diameter of 6 feet. The barrel is filled with oil to 6 inches from the top of the barrel. What is the volume of oil in a barrel?

i got it wrong but the guy who says its 113.04 ft^2 is right

The volume of oil in a barrel is 113.04ft³

Step-by-step explanation:

To calculate the volume of a cylinder we have to use the following formula:

6in = 0.5ft

v = volume

h = height = 4.5ft  - 0.5in = 4ft

π = 3.14

r = radius = 6ft /2 = 3ft

v = (π * r²) * h

we replace the unknowns with the values we know

v = (3.14 * (3ft)²) * 4ft

v = (3.14 * 9ft²) * 4ft

v = 28.26ft² * 4ft

v = 113.04ft³

The volume of oil in a barrel is 113.04ft³

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

step-by-step explanation: