Question

determine the volume of the given sphere. (nearest tenth)
a 91.1 cubic units
b 286.1 cubic units
c 381.5 cubic units
d 401.6 cubic units
(image of a sphere with radius r = 4.5, and formula options: b: v = \frac{4}{3}(3.14)(4.5)^2, c: v = \frac{4}{3}(3.14)(4.5)^3, d: v = (3.14)(4.5)^3)

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Here, \(\pi = 3.14\) and \(r = 4.5\).

Step2: Substitute the values into the formula

Substitute \(r = 4.5\) and \(\pi=3.14\) into \(V=\frac{4}{3}\pi r^{3}\). First, calculate \(r^{3}\): \(r^{3}=(4.5)^{3}=4.5\times4.5\times4.5 = 91.125\). Then, calculate \(\frac{4}{3}\times3.14\times91.125\). \(\frac{4}{3}\times3.14 = 4.1866\cdots\). Then \(4.1866\cdots\times91.125=381.51\approx381.5\)

Answer:

C. \(381.5\) cubic units