β‘ The Questions β‘
-Pia drew a circle with a circumference of C and a diameter of 14 in. Pia knows that C= Οd, and she wrote the following equation to represent the value of Ο.
(a) There is an error in Piaβs equation. Write an equation to correctly represent the value of Ο.
(b) Write an equation and find the circumference of the circle.
Show your work.
-Hank used a semicircle, a rectangle, and a triangle to form the following composite figure. What is its area in square centimeters? Use 3.14 to approximate Ο. Show your work.
-At a zoo, the lion pen is surrounded by a ring-shaped sidewalk. The outer edge of the sidewalk is a circle with a radius of 11m. The inner edge of the sidewalk is a circle with a radius of 9m.
(a) Write and simplify an expression for the exact area of the sidewalk.
(b) Find the approximate area of the sidewalk. Use 3.14 to approximate Ο. Show your work.
* ΰ¨ΰ§ ββββββββββββ ΰ¨ΰ§*
β‘ The Answer(s) β‘
-1 (A) --> N/A!
-1 (B) --> N/A!
-2 (A) --> 1,156 Sq Meters
-3 (A) --> 40Ο Sq Meters
-3 (B) --> 125.6 m^2
*ΰ¨ΰ§ ββββββββββββ ΰ¨ΰ§*
β‘ The Explanation(s)/Step-By-Step(s) β‘
-1 (A) --> N/A!
-1 (B) --> N/A!
-2 (A) --> We can figure out that the rectangle is 50 cm, and the triangle is 26 cm! In order to figure out the circle's cm, we can use the formula Ο x r^2. The radius of the circle is 10 cm, and the Ο is 3.14. We can multiply 3.14 by 10, this makes the number 31.4 cm! If we add the numbers, we end up with the sum of 107.4 cm. Converting 107.4 in Sq Meters leaves us with 1,156 Sq Meters! Therefore, 1,156 Sq Meters is your answer!
-3 (A) --> 125.6 m^2 is equal to 40Ο Sq Meters, This helps determine the exact area.
-3 (B) --> The approximate area of the sidewalk is 125.6 m^2. To solve this, you need to subtract the area of the inner edge of the lion pen from the outer edge of the lion pen.
A = Ο ( (11 m)^2 - (9 m)^2 )
A= Ο ( 121 m^2 - 81 m^2 )
A = Ο ( 40 m^2 )
A= 40Ο m^2. The area of the sidewalk comes out as 40Ο square meters, this is equal to 125.6 m^2, therefore, your answer will be 125.6 m^2.
*ΰ¨ΰ§ ββββββββββββ ΰ¨ΰ§*
β‘ Tips β‘
-Use some formulas!
-Use videos to help!
*ΰ¨ΰ§ ββββββββββββ ΰ¨ΰ§*
β‘ Formulas β‘
A = Ο x r^2 (Radius)
A = 1/2 B x H (Height and Base, Triangle)
A = B x H (Height and Base, Parallelogram)
A = S1 X S2 (Sides, Square)
