Question

question 10 (4 points)
calculate surface area 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 surface area using these measurements. next take the measurements required in the formula and add 0.05 to them. take the new measurements and find the surface area. your answer will be a range from your lowest surface area to your highest surface area.
sphere
surface area = 4πr²
volume = 4/3 πr³
1978.2 mm² ≤ surface area ≤ 2009.9 mm²
1970.2 mm² ≤ surface area ≤ 2000.9 mm²
1977.2 mm² ≤ surface area ≤ 2008.9 mm²
1975.2 mm² ≤ surface area ≤ 2001.9 mm²

Explanation:

Step1: Find the 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 $r_1=r - 0.05=12.6−0.05 = 12.55$ mm.

Step2: Calculate the lower - bound surface area

The surface area formula of a sphere is $A = 4\pi r^{2}$. Substitute $r_1$ into the formula: $A_1=4\times3.14\times(12.55)^{2}=4\times3.14\times157.5025 = 1977.2$ mm².

Step3: Find the upper - bound radius

The upper - bound radius $r_2=r + 0.05=12.6 + 0.05=12.65$ mm.

Step4: Calculate the upper - bound surface area

Substitute $r_2$ into the surface area formula: $A_2=4\times3.14\times(12.65)^{2}=4\times3.14\times160.0225 = 2008.9$ mm².

Answer:

$1977.2$ mm² $\leq$ surface area $\leq2008.9$ mm², so the correct option is: $1977.2$ mm² $\leq$ surface area $\leq2008.9$ mm²