The surface area of a sphere is 7.84π ft.2 What is the radius of this sphere?

Close again!

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.

radius = (7.84π/4π)^(1/2) = 1.5 ft