Question

consider a sphere with a diameter of 10.6 yd. using the aleks calculator, approximate the surface area of the sphere. to do the approximation, use the π button on the calculator, and round your answer to the nearest hundredth. if necessary, refer to the list of geometry formulas. make sure that you use the correct units in your answer. approximate surface area:

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter $d$. Given $d = 10.6$ yd, so $r=\frac{d}{2}=\frac{10.6}{2}=5.3$ yd.

Step2: Use the surface - area formula

The formula for the surface area $A$ of a sphere is $A = 4\pi r^{2}$. Substitute $r = 5.3$ yd into the formula: $A=4\pi(5.3)^{2}$.

Step3: Calculate the value

First, calculate $(5.3)^{2}=28.09$. Then $4\pi(5.3)^{2}=4\pi\times28.09$. Using the $\pi$ button on the calculator, $A = 4\times\pi\times28.09\approx4\times3.14159\times28.09 = 353.9177$.

Step4: Round to the nearest hundredth

Rounding $353.9177$ to the nearest hundredth gives $A\approx353.92$ yd².

Answer:

$353.92$ yd²