The surface area of a sphere is 7.84π ft.2 What is the radius of this sphere?
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SA = 4π r^2
7.84π = 4π r^2
1.96 = r^2
r = 1.4 ft, not 1.5 ft
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the surface area of the sphere is 7.84π ft^2, we can set up the equation:
7.84π ft^2 = 4πr^2
Dividing both sides of the equation by 4π, we have:
(7.84π ft^2) / (4π) = (4πr^2) / (4π)
Simplifying, we get:
(7.84π ft^2) / (4π) = r^2
Canceling out the π on both sides, we have:
7.84 ft^2 / 4 = r^2
Dividing both sides by 4, we get:
1.96 ft^2 = r^2
Taking the square root of both sides, we have:
√(1.96 ft^2) = √(r^2)
Simplifying, we get:
1.4 ft = r
Therefore, the radius of the sphere is 1.4 ft.
To find the radius of a sphere given its surface area, we can use the formula for the surface area of a sphere:
Surface Area = 4πr^2
Given that the surface area is 7.84π ft², we can set up the equation as follows:
7.84π ft² = 4πr^2
Now, we can cancel out the common factor of π from both sides of the equation:
7.84 ft² = 4r^2
Dividing both sides of the equation by 4, we get:
1.96 ft² = r^2
To find the radius, we need to take the square root of both sides of the equation:
√(1.96 ft²) = √(r^2)
The square root of 1.96 ft² is approximately 1.4 ft.
Therefore, the radius of the sphere is 1.4 ft.