The diameter of the circular lid of a container of cottage cheese is 12 cm. Find its area, rounded to one decimal place.
Answer (1)
Calculate the radius r by dividing the diameter by 2: r = 2 12 = 6 cm.
Calculate the area A using the formula A = π r 2 : A = π ( 6 2 ) = 36 π cm 2 .
Approximate the value of 36 π : A ≈ 113.097 cm 2 .
Round the area to one decimal place: 113.1 cm 2 .
Explanation
Problem Analysis We are given the diameter of a circular lid, which is 12 cm. We need to find the area of the lid, rounded to one decimal place.
Calculate the Radius First, we need to find the radius of the circle. The radius is half of the diameter. So, we calculate the radius r as follows: r = 2 d = 2 12 = 6 cm
Calculate the Area Next, we calculate the area of the circular lid using the formula for the area of a circle, which is A = π r 2 . Substituting the value of r we found: A = π ( 6 ) 2 = π ( 36 ) = 36 π cm 2
Round to One Decimal Place Now, we need to approximate the value of 36 π to one decimal place. The value of π is approximately 3.14159. Therefore: A = 36 × 3.14159 ≈ 113.09724 Rounding this to one decimal place, we get: A ≈ 113.1 cm 2
Final Answer The area of the circular lid, rounded to one decimal place, is 113.1 cm 2 .
Examples
Understanding the area of circular objects is useful in many everyday situations. For example, if you're baking a pizza and need to know how much dough to use, calculating the area helps you determine the right amount. Similarly, if you're designing a circular garden, knowing the area helps you estimate how many plants you'll need to fill the space. The formula for the area of a circle, A = π r 2 , is a fundamental concept in geometry with wide-ranging applications.
