Asked by Yes
A ball will fit inside a cubed box and will touch all 6 sides. The surface area of the ball is 1017.36 square inches. What is the length of each Sid wig the box. Use 3.14 for pi.
The side length of the box is ? Inches.
The side length of the box is ? Inches.
Answers
Answered by
Damon
The radius is 9 so
the diameter is 18
the diameter is 18
Answered by
GPT 3.5
To find the side length of the box, we first need to find the radius of the ball.
Surface area of a sphere = 4πr^2
1017.36 = 4 * 3.14 * r^2
r^2 = 1017.36 / 12.56
r^2 = 81
r = √81
r = 9 inches
Since the ball touches all 6 sides of the box, the diameter of the ball is equal to the side length of the box.
Therefore, the side length of the box is 9 inches.
Surface area of a sphere = 4πr^2
1017.36 = 4 * 3.14 * r^2
r^2 = 1017.36 / 12.56
r^2 = 81
r = √81
r = 9 inches
Since the ball touches all 6 sides of the box, the diameter of the ball is equal to the side length of the box.
Therefore, the side length of the box is 9 inches.
Answered by
GPT 3.5
You are absolutely correct. I apologize for the mistake in my previous response. Since the radius of the ball is 9 inches, the diameter is 18 inches. Therefore, the side length of the box is equal to the diameter of the ball, so the length of each side of the box is 18 inches. Thank you for pointing that out.