Asked by Kakashi
Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.2
63.585
in
.
2
and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?(1 point)
Responses
1.2 in. × 1.2 in. × 1.2 in.
1.2
in.
×
1.2
in.
×
1.2
in
.
1.2 inches times 1.2 inches times 1.2 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25
in.
×
2.25
in.
×
2.25
in
.
2.25 inches times 2.25 inches times 2.25 inches
4 in.× 4 in.× 4 in.
4
in.
×
4
in.
×
4
in
.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
63.585
in
.
2
and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?(1 point)
Responses
1.2 in. × 1.2 in. × 1.2 in.
1.2
in.
×
1.2
in.
×
1.2
in
.
1.2 inches times 1.2 inches times 1.2 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25
in.
×
2.25
in.
×
2.25
in
.
2.25 inches times 2.25 inches times 2.25 inches
4 in.× 4 in.× 4 in.
4
in.
×
4
in.
×
4
in
.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
Answers
Answered by
GPT 3.5
4.5
in.
×
4.5
in.
×
4.5
in.
4.5 inches times 4.5 inches times 4.5 inches
in.
×
4.5
in.
×
4.5
in.
4.5 inches times 4.5 inches times 4.5 inches
Answer
why not 4.5 x 4.5 x 4.5?
Answered by
GPT 3.5
I apologize for the confusion. You are correct. The dimensions of the cube box should be 4.5 inches by 4.5 inches by 4.5 inches.
Answer
But why?
Answered by
GPT 3.5
To calculate the dimensions of the cube box, we need to find the side length of the cube.
Since a sphere has a surface area of 63.585 in², we can use the formula for the surface area of a sphere to find the radius, and then convert it to a diameter.
Surface Area of a Sphere = 4πr²
63.585 = 4πr²
Divide both sides by 4π:
r² = 63.585 / (4π) ≈ 5.1
Take the square root of both sides:
r ≈ √5.1 ≈ 2.26
Now we have the radius. To get the diameter, multiply the radius by 2:
d ≈ 2 × 2.26 ≈ 4.52
Since the dimensions of a cube are the same for each side, the cube box should have sides that are approximately 4.52 inches long. Rounded to the nearest tenth, this gives us dimensions of 4.5 inches by 4.5 inches by 4.5 inches.
Since a sphere has a surface area of 63.585 in², we can use the formula for the surface area of a sphere to find the radius, and then convert it to a diameter.
Surface Area of a Sphere = 4πr²
63.585 = 4πr²
Divide both sides by 4π:
r² = 63.585 / (4π) ≈ 5.1
Take the square root of both sides:
r ≈ √5.1 ≈ 2.26
Now we have the radius. To get the diameter, multiply the radius by 2:
d ≈ 2 × 2.26 ≈ 4.52
Since the dimensions of a cube are the same for each side, the cube box should have sides that are approximately 4.52 inches long. Rounded to the nearest tenth, this gives us dimensions of 4.5 inches by 4.5 inches by 4.5 inches.