(in this question they did not give me any diagrams)
use pie 22/7
(a) a piece of wire is bent to form a square of area 121cm squared
Calculate the length of each side of the square.
Calculate the perimeter of the square.
(b) the same piece of wire was bent to form a circle.
Calculate the radius of the circle.
Calculate the area of the circle.
PLEASE EXPLAIN HOW YOU GOT EACH ANSWER THANK YOU.
first, it's "pi" not "pie"
121 = 11^2, so the wire is bent into an 11×11 square. 4 sides of 11cm = 44cm perimeter.
for a circle, the circumference is 2πr, and the area is πr^2. We have 122cm of wire, so c = 121. r = 121/2π = 19.26cm
the area of the circle is πr^2 = π(c/2π)^2 = c^2/4π = 121^2/4π = 1165cm^2
How did you get 122cm of wire??
Come on, Indiana!
Could you not see that Steve made a simple typing error??
He did use the correct number of 121 in the very next line, so clearly no harm was done.
Both his answers are correct.
A piece of wire is bent to form a square of area 121cm.
Calculate:
a)the length of each side of the square
b)the perimeter of the square
The piece of wire is now bent to form a circle using π=3.14
Calculate:
a)The radius of the circle
area of the square = 121cm²
s² = 121
s = square root of 121
s = 11 cm
the length of each side of the square is 11cm.
perimeter of the square = 4s
= 4*11
= 44 cm
length of the wire = c of circle
121 cm = 2πr
121 cm = 2*22/7* r
r = 121 by 2 * 22/7
r = 19.26 cm
therefore,
area of the circle = πr²
= 22/7 * 19.26 * 19.26
= 1165 cm²
thank you!!
(a) To find the length of each side of the square, we need to calculate the square root of the area. Since the given area is 121 cm², we can use the formula:
Side length = √(Area)
Plugging in the given value:
Side length = √(121)
Since 121 is a perfect square, the square root is a whole number:
Side length = 11 cm
To calculate the perimeter of the square, we know that all four sides are equal in length. Therefore:
Perimeter = 4 * Side length
Substituting the value of the side length we found earlier:
Perimeter = 4 * 11
Perimeter = 44 cm
(b) To find the radius of the circle, we need to use the perimeter of the square from part (a) since the wire was used to form the circle. The formula to calculate the radius of a circle given its perimeter (P) is:
Radius = P / (2π)
Using the value of the perimeter we found earlier:
Radius = 44 / (2 * 22/7)
Simplifying:
Radius = 44 / (44/7)
Dividing by a fraction is equivalent to multiplying by its reciprocal:
Radius = 44 * (7/44)
Canceling out 44:
Radius = 7 cm
To calculate the area of the circle, we can use the formula:
Area = π * Radius²
Substituting the value of the radius we found earlier:
Area = 22/7 * (7)²
Area = 22/7 * 49
Area = 154 cm²
So, the radius of the circle is 7 cm and the area of the circle is 154 cm².