Answer :
To determine the radius of the circle given by the equation [tex]\( x^2 + y^2 = 64 \)[/tex], follow these steps:
1. Understand the Standard Form of the Circle Equation: The general form of a circle centered at the origin (0,0) is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
In this equation, [tex]\( r \)[/tex] represents the radius of the circle.
2. Identify the Given Equation: The given circle equation is:
[tex]\[ x^2 + y^2 = 64 \][/tex]
3. Relate the Given Equation to the Standard Form: By comparing the given equation [tex]\( x^2 + y^2 = 64 \)[/tex] to the standard form [tex]\( x^2 + y^2 = r^2 \)[/tex], we see that:
[tex]\[ r^2 = 64 \][/tex]
4. Solve for the Radius [tex]\( r \)[/tex]: To find the radius [tex]\( r \)[/tex], take the square root of both sides of the equation:
[tex]\[ r = \sqrt{64} \][/tex]
5. Calculate the Square Root: The square root of 64 is:
[tex]\[ \sqrt{64} = 8 \][/tex]
Therefore, the radius of the circle is [tex]\( \boxed{8} \)[/tex]. This corresponds to option A.
1. Understand the Standard Form of the Circle Equation: The general form of a circle centered at the origin (0,0) is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
In this equation, [tex]\( r \)[/tex] represents the radius of the circle.
2. Identify the Given Equation: The given circle equation is:
[tex]\[ x^2 + y^2 = 64 \][/tex]
3. Relate the Given Equation to the Standard Form: By comparing the given equation [tex]\( x^2 + y^2 = 64 \)[/tex] to the standard form [tex]\( x^2 + y^2 = r^2 \)[/tex], we see that:
[tex]\[ r^2 = 64 \][/tex]
4. Solve for the Radius [tex]\( r \)[/tex]: To find the radius [tex]\( r \)[/tex], take the square root of both sides of the equation:
[tex]\[ r = \sqrt{64} \][/tex]
5. Calculate the Square Root: The square root of 64 is:
[tex]\[ \sqrt{64} = 8 \][/tex]
Therefore, the radius of the circle is [tex]\( \boxed{8} \)[/tex]. This corresponds to option A.
