Which statement correctly describes the relationship shown in the cylinder area formula for the ends?

Which statement correctly describes the relationship shown in the cylinder area formula for the ends?

• A. 2πr^2 represents the ends
• B. πdh represents the ends
• C. 2πrh represents the ends
• D. πd^2 represents the ends

Answer: (A)

Ends of a cylinder are two circles, so you use the circle area formula. The area of one circle is π times the radius squared, and there are two ends, so you double that: 2πr^2. That matches the description for the ends. The other expressions describe other parts of the cylinder. πdh (or equivalently πd h) is a way to write the lateral (side) area when using diameter, since the circumference is πd and multiplying by height gives the side area. The lateral area is 2πrh, which is not the ends. πd^2 would be four times the actual circle area if you tried to express a circle’s area purely in terms of diameter, since the true circle area is π(d/2)^2 = πd^2/4. So the ends are correctly described by 2πr^2.

Ends of a cylinder are two circles, so you use the circle area formula. The area of one circle is π times the radius squared, and there are two ends, so you double that: 2πr^2. That matches the description for the ends.

The other expressions describe other parts of the cylinder. πdh (or equivalently πd h) is a way to write the lateral (side) area when using diameter, since the circumference is πd and multiplying by height gives the side area. The lateral area is 2πrh, which is not the ends. πd^2 would be four times the actual circle area if you tried to express a circle’s area purely in terms of diameter, since the true circle area is π(d/2)^2 = πd^2/4. So the ends are correctly described by 2πr^2.