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The Pranger Metal Company makes solid cylindrical steel rods by meltin
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05 Dec 2022, 01:58
05 Dec 2022, 01:58
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The Pranger Metal Company makes solid cylindrical steel rods by melting down blocks of steel and pouring the melted steel into molds. Each cylindrical rod has a diameter of 14 inches and a height of 8 inches, and the dimensions of each steel block are 2 feet by 12 feet by 15 feet. If no steel is lost in the production process, how many complete cylinders can be made from a single block of steel?
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505
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Re: The Pranger Metal Company makes solid cylindrical steel rods by meltin
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07 Dec 2022, 11:01
07 Dec 2022, 11:01
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Carcass wrote:
The Pranger Metal Company makes solid cylindrical steel rods by melting down blocks of steel and pouring the melted steel into molds. Each cylindrical rod has a diameter of 14 inches and a height of 8 inches, and the dimensions of each steel block are 2 feet by 12 feet by 15 feet. If no steel is lost in the production process, how many complete cylinders can be made from a single block of steel?
Show: ::
505
Let the number of cylinders be \(N\)
If no steel is lost in the production process ...
Thus means Volume of block = Volume on \(N\) cylinders
(2 x 12)(12 x 12)(15 x 12) = N x \(π(7^2)8\)
Solve for N = 505
NOTE: Since the dimensions of the block are in feet, we need to multiply each of the dimension with 12 in order to converst them into inches.
Re: The Pranger Metal Company makes solid cylindrical steel rods by meltin
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09 Dec 2022, 03:00
09 Dec 2022, 03:00
Expert Reply
OE
To find the number of cylinders that can be made from one block of steel, divide the volume of the block by the volume of a cylinder. Start by converting the dimensions of the block into inches: Each steel block is 24 inches by 144 inches by 180 inches, so the volume is 24 × 144 × 180 = 622,080. The formula for the volume of a cylinder is V = πr2h, so the volume of each cylinder is π × 72 × 8 = 1,230.88. Finally, 622,080 ÷ 1,230.88 = 505.395; the problem asked for complete cylinders, so the correct answer is 505.
To find the number of cylinders that can be made from one block of steel, divide the volume of the block by the volume of a cylinder. Start by converting the dimensions of the block into inches: Each steel block is 24 inches by 144 inches by 180 inches, so the volume is 24 × 144 × 180 = 622,080. The formula for the volume of a cylinder is V = πr2h, so the volume of each cylinder is π × 72 × 8 = 1,230.88. Finally, 622,080 ÷ 1,230.88 = 505.395; the problem asked for complete cylinders, so the correct answer is 505.
