Find the surface area of a sphere with a circumference of 40 ft. Round to the nearest tenth.

Solution:

The surface area of a sphere is given by the formula 4πr² where r = radius of the sphere.

The circumference of the sphere is given as 40 ft. The circumference of the sphere is denoted by C which is equal to:

C = 2πr

Since C = 40 ft , we can write

40 = 2πr

The radius r  = 40/(2π) 

                     = 20/π------>(1)

Therefore the surface area of the sphere is determined as:

Surface Area = A = 4πr²

From (1) we have r = 20/π. Substituting the value of r in formula of surface area we have:

A  = 4π(20/π)²

=  80/π

= 80 ×( 7/22)(π = 22/7)

=  40 × (7/11)

=  280/11

=   25.45 ft²

 ≈25.5 ft²

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Find the surface area of a sphere with a circumference of 40 ft. Round to the nearest tenth.

Summary:

The surface area of a sphere with a circumference of 40 ft is 25.5 ft²