Question

question 15 (4 points) calculate volume within 0.1 of the unit used. use 3.14 for pi. to find the numbers within 0.1 of the unit used, take 0.1 and divide by 2. 0.1/2 is 0.05. take each measurement required in the formula and subtract 0.05 from them. then find the volume using these measurements. next take the measurements required in the formula and add 0.05 to them. take the new measurements and find the volume. your answer will be a range from your lowest volume to your highest volume. sphere surface area = 4πr² volume = 4/3 πr³ 8275.6 mm³ ≤ volume ≤ 8485.0 mm³ 8175.6 mm³ ≤ volume ≤ 8375.0 mm³ 8234.6 mm³ ≤ volume ≤ 8475.0 mm³ 8275.6 mm³ ≤ volume ≤ 8475.0 mm³

Explanation:

Step1: Find lower - bound radius

The given diameter is $d = 25.2$ mm, so the nominal radius $r=\frac{d}{2}=12.6$ mm. The lower - bound radius $r_{min}=12.6 - 0.05=12.55$ mm.

Step2: Calculate lower - bound volume

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = r_{min}=12.55$ mm and $\pi = 3.14$ into the formula:
$V_{min}=\frac{4}{3}\times3.14\times(12.55)^{3}=\frac{4\times3.14\times1978.543875}{3}\approx8275.6$ mm³.

Step3: Find upper - bound radius

The upper - bound radius $r_{max}=12.6 + 0.05 = 12.65$ mm.

Step4: Calculate upper - bound volume

Substitute $r = r_{max}=12.65$ mm and $\pi = 3.14$ into the volume formula $V=\frac{4}{3}\pi r^{3}$:
$V_{max}=\frac{4}{3}\times3.14\times(12.65)^{3}=\frac{4\times3.14\times2019.019625}{3}\approx8475.0$ mm³.

Answer:

$8275.6$ mm³ $\leq$ volume $\leq8475.0$ mm³