Question

1. a formula for the volume v of a sphere with radius r is v = \frac{4}{3}\pi r^{3}. if the radius of a spherical rubber ball is 1\frac{1}{4} inches, what is its volume to the nearest cubic inch? a. 5 b. 7 c. 8 d. 16 e. 65

Explanation:

Step1: Convert the radius to decimal

The radius $r = 1\frac{1}{4}=\frac{5}{4}=1.25$ inches.

Step2: Substitute into volume formula

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 1.25$ into it: $V=\frac{4}{3}\pi(1.25)^{3}$.

Step3: Calculate $(1.25)^{3}$

$(1.25)^{3}=1.25\times1.25\times1.25 = 1.953125$.

Step4: Calculate $\frac{4}{3}\pi(1.25)^{3}$

$V=\frac{4}{3}\times\pi\times1.953125\approx\frac{4}{3}\times3.14\times1.953125$. First, $\frac{4}{3}\times3.14\approx4.1867$, then $4.1867\times1.953125\approx8$.

Answer:

C. 8