The price of the steel rod varies jointly as the length and the square of the diameter. If a 12 feet rod with the 2 inches of the diameter cost 480 then what is the price of an 18 with three inches of diameter?
x/(18*3^2) = 480/(12*2^2)
500
To find the price of an 18 feet rod with a three-inch diameter, we can use the concept of joint variation. Joint variation states that if a quantity varies jointly with two other quantities, its value can be found by multiplying the values of those two quantities together, along with a constant of variation.
Let's break down the given information:
- The price of the steel rod varies jointly as the length and the square of the diameter.
- A 12 feet rod with a 2-inch diameter costs 480.
To find the constant of variation, we can set up a proportion using the given information:
(price of the first rod) / (length of the first rod * (diameter of the first rod)^2) = (price of the second rod) / (length of the second rod * (diameter of the second rod)^2)
Plugging in the known values:
480 / (12 * 2^2) = (price of the second rod) / (18 * 3^2)
Simplifying:
480 / 48 = (price of the second rod) / 162
Solving for the price of the second rod:
(price of the second rod) = (480 / 48) * 162
(price of the second rod) = 16 * 162
(price of the second rod) = 2592
Therefore, the price of an 18 feet rod with a three-inch diameter is 2592.
To find the price of an 18 feet rod with a three-inch diameter, we can use the concept of joint variation. When two variables vary jointly, it means their product is constant. In this case, the price varies jointly with the length and the square of the diameter.
Let's set up the equation using the given information:
Price1 = $480 (for the 12 feet rod with the 2-inch diameter)
Length1 = 12 feet
Diameter1 = 2 inches
Price2 = ?
Length2 = 18 feet
Diameter2 = 3 inches
Using joint variation, we have:
Price1 * (Length1 * (Diameter1^2)) = Price2 * (Length2 * (Diameter2^2))
Plugging in the given values, we get:
$480 * (12 * (2^2)) = Price2 * (18 * (3^2))
Simplifying this equation, we have:
$480 * (12 * 4) = Price2 * (18 * 9)
$480 * 48 = Price2 * 162
To find the value of Price2, we divide both sides of the equation by 162:
Price2 = ($480 * 48) / 162
Calculating this, we get:
Price2 = $142.22 (rounded to the nearest cent)
Therefore, the price of an 18 feet rod with a three-inch diameter is approximately $142.22.