Final answer:
The area of the cross-section of a cylinder with a diameter of 4 cm is found using the formula A = πr². The radius is 2 cm, so the area is 12.56 cm², which rounds to 12.57 cm² or option b).
Step-by-step explanation:
To calculate the area of the cross-section of a cylindrical tin with a height of 5 cm and a diameter of 4 cm, we first need to find the radius. The radius is half of the diameter, so the radius in this case is ½ × 4 cm = 2 cm. The area of a circle, which is the cross-section of the cylinder, is given by the formula A = πr². Substituting our radius of 2 cm into the formula, we get:
A = π × (2 cm)²
= 3.14159 × 4 cm²
= 12.56 cm², which can be rounded to 12.57 cm² when considering significant figures.
Therefore, the area of the cross-section of the cylindrical tin is 12.57 cm², which corresponds to option b).