The area A of a cross section through the center of a sphere is 32in^2. Find the surface area of the sphere.
area = πr^2 = 32
surface area of a sphere = 4πr^2
= 4(32) = 128 cm^2
Why did the sphere go to therapy? Because it had some "sphere issues"!
But don't worry, I'm here to help with your question. The surface area of a sphere can be found using the equation A = 4πr².
Since we know the area of the cross section is 32in², we can set up an equation to solve for the radius (r):
32 = 4πr²
To isolate r², we'll divide both sides by 4π:
8 = πr²
Then divide by π:
8/π = r²
Now, we can find the value of r by taking the square root of both sides:
√(8/π) = r
Finally, to find the surface area (SA), we can substitute the value of r into the equation SA = 4πr²:
SA = 4π(√(8/π))²
Simplifying this, we get:
SA = 4π(8/π)
SA = 32 in²
So, the surface area of the sphere is 32 square inches. Hope that answers your question with a little comedic twist!
To find the surface area of a sphere, we need to know either the radius or the diameter. However, the given information about the cross section area is not enough to directly calculate the surface area of the sphere.
Is there any other information given in the problem?
To find the surface area of a sphere, you need to use the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
In this case, we are given the area A of a cross section, which is the area of a circle. The area of a circle can be found using the formula:
A = πr^2
Since the cross section goes through the center of the sphere, the radius of the circle is the same as the radius of the sphere. Therefore, we can equate the area of the cross section to the area of a circle to get:
A = πr^2
Given that the area A is 32 in^2, we can solve for r by rearranging the equation:
32 = πr^2
Dividing both sides by π, we get:
r^2 = 32/π
Now, take the square root of both sides to find the value of r:
r = √(32/π)
With the value of r, we can now calculate the surface area of the sphere using the formula:
Surface Area = 4πr^2
Substituting the value of r, we have:
Surface Area = 4π(√(32/π))^2
Now, simplify the expression inside the parentheses:
Surface Area = 4π(32/π)
The π in the numerator and denominator cancels out, leaving:
Surface Area = 4(32)
Calculating this expression gives us:
Surface Area = 128 square inches
Therefore, the surface area of the sphere is 128 square inches.