A cereal company wants to enlarge the volume of the cylindrical container used for one of its products by enlarging the radius of the cylinder. The height must be 20 centimeters. The new volume of the cylinder is given by the equation V(x)=20π(5+x)2.where x is the additional length of the radius in centimeters. Which of the following equivalent expressions displays the current volume of the cylinder as a constant or coefficient?Choose 1 answer:(A) 20πx2+200πx+500π(B) 20π(x2+10x+25)(C) 20π(x2+10x+25)(D) 20πx2+200πx+500π
Q. A cereal company wants to enlarge the volume of the cylindrical container used for one of its products by enlarging the radius of the cylinder. The height must be 20 centimeters. The new volume of the cylinder is given by the equation V(x)=20π(5+x)2.where x is the additional length of the radius in centimeters. Which of the following equivalent expressions displays the current volume of the cylinder as a constant or coefficient?Choose 1 answer:(A) 20πx2+200πx+500π(B) 20π(x2+10x+25)(C) 20π(x2+10x+25)(D) 20πx2+200πx+500π
Understand Equation: Understand the given equation for the new volume of the cylinder.The equation provided is V(x)=20π(5+x)2, which represents the volume of the cylinder after increasing the radius by x centimeters. The current volume of the cylinder can be found by setting x to 0, since x is the additional length added to the original radius.
Calculate Current Volume: Calculate the current volume of the cylinder by setting x to 0 in the given equation.V(0)=20π(5+0)2V(0)=20π(5)2V(0)=20π(25)V(0)=500πThis calculation gives us the current volume of the cylinder as a constant, which is 500π cubic centimeters.
Compare with Answer Choices: Compare the result from Step 2 with the given answer choices to find the equivalent expression.We are looking for an expression that has the constant 500π as part of it when x is 0. Let's check each option:(A) π(20x2+200x+500) - When x=0, this simplifies to π(500), which matches our calculation.(B) 20π(x2+10x+10)+3 - This does not simplify to 500π when x=0.(C) 20π(x2+10x+25) - This does not simplify to 500π when x=0.(D) x2 - This simplifies to 500π when x=0, but it is not written as a single expression with a constant or coefficient.The correct answer is the one that simplifies to 500π when x=0 and is written as a single expression with a constant or coefficient. Option (A) meets these criteria.
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