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A cylinder with a base diameter of x units has a volume of πx3 cubic units.
A cylinder with a base diameter of x units has a volume of pi x cubed cubic units.
Which statements about the cylinder are true? Select two options.
The radius of the cylinder is 2x units.
The area of the cylinder’s base is One-fourthπx2 square units.
The area of the cylinder’s base is One-halfπx2 square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
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True statements:
- The area of the cylinder’s base is One-fourth πx^2 square units.
- The height of the cylinder is 4x units.
Reasoning:
Diameter = x ⇒ radius r = x/2. Base area = πr^2 = π(x/2)^2 = πx^2/4.
Volume V = base area × height ⇒ πx^3 = (πx^2/4)·h, so h = (πx^3)/(πx^2/4) = 4x.
- The area of the cylinder’s base is One-fourth πx^2 square units.
- The height of the cylinder is 4x units.
Reasoning:
Diameter = x ⇒ radius r = x/2. Base area = πr^2 = π(x/2)^2 = πx^2/4.
Volume V = base area × height ⇒ πx^3 = (πx^2/4)·h, so h = (πx^3)/(πx^2/4) = 4x.
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