what is the volume of a sphere with a radius of 34.2 m, rounded to the nearest tenth of a cubic meter?
what is the volume of a sphere with a radius of 34.2 m, rounded to the nearest tenth of a cubic meter?
Answer
Explanation:
Step1: Recall the formula for the volume of a sphere
The formula for the volume ( V ) of a sphere is ( V=\frac{4}{3}\pi r^{3} ), where ( r ) is the radius of the sphere.
Step2: Substitute the given radius into the formula
Given that ( r = 34.2\space m ), we substitute ( r ) into the formula: ( V=\frac{4}{3}\pi(34.2)^{3} ) First, calculate ( (34.2)^{3} ): ( 34.2\times34.2\times34.2 = 34.2\times(34.2\times34.2)=34.2\times1169.64 = 39991.688 ) Then, multiply by ( \frac{4}{3}\pi ): ( V=\frac{4}{3}\pi\times39991.688 ) ( V=\frac{4\times39991.688}{3}\pi=\frac{159966.752}{3}\pi\approx53322.2507\times\pi ) Using ( \pi\approx3.14159 ), we get: ( V\approx53322.2507\times3.14159\approx167537.9 ) (rounded to the nearest tenth)
Answer:
The volume of the sphere is approximately ( 167537.9 \space m^{3} )