Final answer:
The area of a cylindrical shape with a height of 5 and a radius of 2 is calculated using the formula A = 2πrh for the lateral surface area. The calculated area is 20π, which approximates to 63 when rounded to two significant figures.
Step-by-step explanation:
To find the area of a shape based on the given dimensions, namely a height of 5 and a radius of 2, we need to determine the type of shape we're dealing with. Since only a height and radius are provided, it is possible that the shape is a cylinder. The area of a cylinder can be calculated using the formula for the lateral surface area, which is A = 2πrh, or the total surface area, which includes both the circular top and bottom in addition to the lateral surface. For a cylinder, the total surface area formula is A = 2πr² + 2πrh. Assuming we are finding the lateral surface area, we calculate it as follows:
A = 2π(2)(5)
= 2(3.1415927...)(2)(5)
= 20π
= 20(3.1415927...)
= 62.83185307
Since the radius is only given to one decimal place, we round our answer to two significant figures, which gives us:
A=63 (to two significant figures).