An artist was planning a new painting and decided to paint circles. His plan is shown below.
A large circle has two smaller circles inside of it. The smallest circle touches the very top of the large circle. The medium circle touches the bottom of the small circle and the bottom of the large circle. There is a dotted line stretching from the top to the bottom of the large circle, going through the middle of each of the two circles inside of the large circle. The small circle has a measurement of 3 cm next to the line and the medium circle has a measurement of 7 cm.
Which measurement is closest to the area of the largest circle? Use 3.14 for 𝜋.
An artist was planning a new painting and decided to paint circles. His plan is shown below.
A large circle has two smaller circles inside of it. The smallest circle touches the very top of the large circle. The medium circle touches the bottom of the small circle and the bottom of the large circle. There is a dotted line stretching from the top to the bottom of the large circle, going through the middle of each of the two circles inside of the large circle. The small circle has a measurement of 3 cm next to the line and the medium circle has a measurement of 7 cm.
Which measurement is closest to the area of the largest circle? Use 3.14 for 𝜋.
78.5 cm2
31.4 cm2
284.6 cm2
62.8 cm2
To solve this problem, we need to find the radius of each circle and then use the formula for the area of a circle to calculate the area of the largest circle.
The smallest circle has a measurement of 3 cm, so its radius is 3/2 = 1.5 cm.
The medium circle has a measurement of 7 cm, so its radius is 7/2 = 3.5 cm.
To find the radius of the largest circle, we can add the radii of the smaller circles: 1.5 cm + 3.5 cm = 5 cm.
Using the formula for the area of a circle (A = πr^2), we can find the area of the largest circle:
A = 3.14 * (5 cm)^2 = 3.14 * 25 cm^2 = 78.5 cm^2.
Therefore, the closest measurement to the area of the largest circle is 78.5 cm^2.