Question

question 4 of 5
two points a(1, 3) and b(8, 8) are on opposite sides of the diameter of a sphere. calculate the radius of this sphere, giving your answer correct to 2 decimal places, if necessary.

Explanation:

Step1: Calculate the diameter length

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 1,y_1 = 3,x_2 = 8,y_2 = 8$. So the diameter $d=\sqrt{(8 - 1)^2+(8 - 3)^2}=\sqrt{7^2+5^2}=\sqrt{49 + 25}=\sqrt{74}$.

Step2: Calculate the radius

The radius $r=\frac{d}{2}$. Since $d=\sqrt{74}$, then $r=\frac{\sqrt{74}}{2}\approx\frac{8.6023}{2}=4.30$.

Answer:

$4.30$