1. What is the area of a circle with a diameter of 12.6 in.?Use 3.14 for pi and round your final answer to the nearest hundredth.2. Which explanation can be used to derive the formula for the circumference of a circle? a. Find the difference between the length of the circumference and diameter. Set up an equation showing the relationship of the circumference to diameter to the difference. Rearrange the equation to solve for the circumference. Substitute the diameter with 2 times the radius.b. First find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately π times. Use this relationship to write an equation showing the ratio of circumference to diameter equaling π . Then rearrange the equation to solve for the circumference. Substitute the diameter for 2 times the radius.c. Find the length of the diameter and double this length. Multiply this length by π and set equal the to the circumference. Substitute the diameter for 2 times radius.d. Find the ratio of the diameter to the area of the circle. Use this ratio to set up an equation to show this ratio equaling π . Substitute the area with 3 times the circumference. Then rearrange the equation to equal to the circumference.3. the attatchment below.4. What is the area of a circle whose radius is 4 ft?a 4π ft²b 8π ft²c 16π ft²d 64π ft²5. The circumference of a circle is 7π m.What is the area of the circle?a 3.5π m²b 12.25π m²c 14π m²c 49π m²
Accepted Solution
A:
Answer:Part 1) [tex]A=124.63\ in^{2}[/tex]Part 2) Option bPart 3) As n increases, ns get closer to [tex]2\pi r[/tex] Part 4) Option c [tex]16\pi\ ft^{2}[/tex]Part 5) Option b. [tex]12.25\pi\ m^{2}[/tex]Step-by-step explanation:Part 1) What is the area of a circle with a diameter of 12.6 in.?we know thatthe area of a circle is equal to[tex]A=\pi r^{2}[/tex] we have[tex]r=12.6/2=6.3\ in[/tex] -----> the radius is half the diametersubstitute the values[tex]A=(3.14)(6.3^{2})=124.63\ in^{2}[/tex] Part 2) Which explanation can be used to derive the formula for the circumference of a circle?First find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately π times. Use this relationship to write an equation showing the ratio of circumference to diameter equaling πso[tex]\frac{C}{D}=\pi[/tex]Rearrange the equation to solve for the circumference[tex]C=\pi D[/tex]Substitute the diameter for 2 times the radius[tex]D=2r[/tex][tex]C=2\pi r[/tex] Part 3) we know thatIf n increases thenthe product ns get closer to the circumference of the circlesothe circumference of a circle is equal to [tex]C=2\pi r[/tex] therefore As n increases, ns get closer to [tex]2\pi r[/tex] Part 4) What is the area of a circle whose radius is 4 ft?we know thatthe area of a circle is equal to[tex]A=\pi r^{2}[/tex]we have[tex]r=4\ ft[/tex] substitute the values[tex]A=(\pi)(4^{2})=16\pi\ ft^{2}[/tex]Part 5) The circumference of a circle is 7π m.What is the area of the circle?we know thatThe circumference of a circle is equal to[tex]C=2\pi r[/tex]we have[tex]C=7\pi\ m[/tex] substitute and solve for r[tex]7\pi=2\pi r[/tex][tex]r=3.5\ m[/tex]Find the area of the circlethe area of a circle is equal to[tex]A=\pi r^{2}[/tex]substitutethe area of a circle is equal to[tex]A=\pi (3.5^{2})=12.25\pi\ m^{2}[/tex]