Question

Please Help Me!
A sphere's center is located at (0,0,0). The point (4,9,-5) is located on the surface of the sphere. Find the length of the radius of the sphere. Round to the nearest tenth.

Answer 1

Answer:

The length of the radius of the sphere is 11.0 units

Step-by-step explanation:

we know that

To calculate the radius of the sphere, we can use the distance formula

$d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}$

where

d is the length of the radius

(x_1,y_1,z_1) is the center of the sphere

and

(x_2,y_2,z_2) is one point on the surface of the sphere

we have

$(x_1,y_1,z_1)=(0,0,0)$

$(x_2,y_2,z_2)=(4,9,-5)$

substitute in the formula

$d=\sqrt{(4-0)^{2}+(9-0)^{2}+(-5-0)^{2}}$

$d=\sqrt{(4)^{2}+(9)^{2}+(-5)^{2}}$

$d=\sqrt{122}$

$d=11.0\ units$

therefore

The length of the radius of the sphere is 11.0 units