Question

the diameter d of a sphere is 18.2 mm. calculate the spheres surface area a. use the value 3.14 for π, and round your answer to the nearest tenth.

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter. Given $D = 18.2$ mm, so $r=\frac{D}{2}=\frac{18.2}{2}=9.1$ mm.

Step2: Use the surface - area formula

The surface - area formula of a sphere is $A = 4\pi r^{2}$. Substitute $r = 9.1$ mm and $\pi=3.14$ into the formula:
$A=4\times3.14\times(9.1)^{2}$.
First, calculate $(9.1)^{2}=9.1\times9.1 = 82.81$.
Then, $4\times3.14\times82.81=12.56\times82.81$.
$12.56\times82.81 = 1040.0936$.

Step3: Round the answer

Round $1040.0936$ to the nearest tenth. The digit in the hundredth place is 9, so we round up the digit in the tenth place. So $A\approx1040.1$ $mm^{2}$.

Answer:

$1040.1$