Question

question 14 (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. right circular cylinder surface area = (2πr²)+(π2rh) volume = πr²h 477.5 in³ ≤ volume ≤ 517.6 in³ 487.5 in³ ≤ volume ≤ 512.6 in³ 487.5 in³ ≤ volume ≤ 517.6 in³ 488.5 in³ ≤ volume ≤ 514.6 in³

Explanation:

Step1: Calculate lower - bound radius and height

The given diameter is 8 in, so the radius $r = 4$ in and height $h=10$ in. The adjustment value is 0.05. The lower - bound radius $r_1=4 - 0.05=3.95$ in and lower - bound height $h_1 = 10-0.05 = 9.95$ in.

Step2: Calculate lower - bound volume

Using the volume formula for a cylinder $V=\pi r^{2}h$, with $\pi = 3.14$, we have $V_1=3.14\times(3.95)^{2}\times9.95=3.14\times15.6025\times9.95=3.14\times155.244875\approx487.5$ in³.

Step3: Calculate upper - bound radius and height

The upper - bound radius $r_2=4 + 0.05 = 4.05$ in and upper - bound height $h_2=10 + 0.05=10.05$ in.

Step4: Calculate upper - bound volume

Using the volume formula $V=\pi r^{2}h$, we have $V_2=3.14\times(4.05)^{2}\times10.05=3.14\times16.4025\times10.05=3.14\times164.845125\approx517.6$ in³.

Answer:

$487.5$ in³ $\leq$ volume $\leq517.6$ in³, so the correct option is: $487.5$ in³ $\leq$ volume $\leq517.6$ in³