This question is not correctly written.
Correct Question
Juan wants to know the cross- sectional area of a circular pipe. He measures the diameter which he finds, to the nearest millimeter, to be 5 centimeters. To find the area of the circle, Juan uses the formula A=〖πr〗^2 where A is the area of the circle and r is its radius. He uses 3.14 for π.
a) What value does Juan get for the area of the circle? Make sure you include your units.
b) Michelle found the area of a circle as 78.5 〖in〗^2. She used 3.14 for π. What is the radius of the circle?
Answer:
a)The Area of the circle is 1962.5 millimeters ²
b) The radius of the circle is
5inches( in)
Step-by-step explanation:
a) The formula for the Area of a circle = πr²
The diameter of the circle was measured by Juan to the nearest millimeters = 5 centimeters
The first step is to convert 5cm to millimeters
1 centimetre = 10 millimeters
5 centimetres =
Cross multiply
= 5 × 10 millimeters
Therefore, 5 centimetres = 50 millimeters.
Since the Diameter of the circle = 50 millimeters,
Radius is calculated as Diameter ÷ 2
Therefore , the radius of the circle = 50 millimeters ÷ 2
= 25 millimeters.
The second step is to find the Area of the circle.
Area of the circle = πr²
Juan used 3.14 for π
Therefore , Area of the circle is calculated as:
= 3.14 ×(25millimeters)²
= 3.14 × 625 millimeters²
= 1962.5 millimeter ²
The Area of the circle is 1962.5 millimeters²
b) Michelle found the area of a circle as 78.5 〖in〗^2. She used 3.14 for π. What is the radius of the circle?
The formula to calculate the Area of a Circle is given as:
A( Area of a circle) = πr²
Since we are asked to find the radius of the circle in Part B, we can derive the formula to find the radius of a circle
A = πr²
r² = A ÷ π
r = √A÷ π
Therefore , the formula to find the Radius of a circle is given as :
r = √A ÷ π
Already given in the question are the following values :
Area of the circle = 78.5inches²
π = Michelle used 3.14
The radius of the circle
= r = √A ÷ π
r = √78.5 in² ÷ 3.14
r = √ 25
r = 5inches( in)
Therefore the radius of the circle is
5inches(in).
