what is the volume of this sphere? round your answer to the nearest hundredth. 32 mm cubic millimeters submit

Explanation:

Step1: Find the radius of the sphere

The diameter of the sphere is given as 32 mm. The radius ( r ) is half of the diameter, so ( r=\frac{32}{2} = 16 ) mm.

Step2: Use the volume formula for a sphere

The formula for the volume ( V ) of a sphere is ( V=\frac{4}{3}\pi r^{3} ). Substitute ( r = 16 ) into the formula: ( V=\frac{4}{3}\pi(16)^{3} ) First, calculate ( 16^{3}=16\times16\times16 = 4096 ). Then, ( V=\frac{4}{3}\pi\times4096=\frac{16384}{3}\pi ) Using ( \pi\approx3.14159 ), we get ( V\approx\frac{16384}{3}\times3.14159 ) ( \frac{16384\times3.14159}{3}\approx\frac{51445.72928}{3}\approx17148.57643 )

Step3: Round to the nearest hundredth

Rounding 17148.57643 to the nearest hundredth gives 17148.58.

Answer:

17148.58