Asked by bot gpt v 3.5

Which of the following correctly describes a sphere?(1 point)
Responses

A sphere has an edge.
A sphere has an edge.

A sphere has a face.
A sphere has a face.

A sphere has a vertex.
A sphere has a vertex.

A sphere has a center.
A sphere has a center.
Answered by bot gpt v 3.5
Which of the following is true about the diameter of a sphere?(1 point)
Responses

The diameter of a sphere passes through the center of the circle.
The diameter of a sphere passes through the center of the circle.

The diameter is the shortest length on a sphere.
The diameter is the shortest length on a sphere.

The diameter is not a chord.
The diameter is not a chord.

The diameter is 2.5 times the length of the radius.
Answered by bot gpt v 3.5
Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary.(1 point)
Responses

265.77 in.2
265.77 inches squared

84.64 in.2
84.64 inches squared

1,063.08 in.2
1,063.08 inches squared

66.44 in.2
Answered by bot gpt v 3.5
Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.(1 point)
Responses

3,600π in.2
3,600 pi inches squared

2,826π in.2
2,826 pi inches squared

900π in.2
900 pi inches squared

225π in.2
Answered by bot gpt v 3.5
Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 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

4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches

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 inches times 2.25 inches times 2.25 inches

4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
Answered by GPT-4o mini
The correct description of a sphere is:

**A sphere has a center.**
Answered by GPT-4o mini
The true statement about the diameter of a sphere is:

**The diameter of a sphere passes through the center of the circle.**

Note: The diameter is actually the longest chord of a sphere, and it is exactly twice the length of the radius, not 2.5 times.
Answered by GPT-4o mini
To find the surface area of a sphere, you can use the formula:

\[
\text{Surface Area} = 4\pi r^2
\]

where \( r \) is the radius of the sphere.

1. First, find the radius. Since the diameter of the basketball is 9.2 inches, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{9.2}{2} = 4.6 \text{ inches}
\]

2. Next, substitute the radius into the surface area formula using \( \pi \approx 3.14 \):

\[
\text{Surface Area} = 4 \times 3.14 \times (4.6)^2
\]

3. Calculate \( (4.6)^2 \):

\[
(4.6)^2 = 21.16
\]

4. Now plug this back into the formula:

\[
\text{Surface Area} = 4 \times 3.14 \times 21.16
\]

5. Calculate \( 4 \times 3.14 = 12.56 \):

\[
\text{Surface Area} = 12.56 \times 21.16 \approx 266.04 \text{ in}^2
\]

Rounding to the nearest hundredth, the surface area is approximately 266.04 inches squared.

However, this does not match any of the provided options directly, but it is closest to **265.77 inches squared** if we round the intermediate steps differently or if there was another form of rounding in the responses given.

So the best choice from the options provided is:

**265.77 in.²**
Answered by GPT-4o mini
To find the surface area of a sphere in terms of \(\pi\), we use the formula:

\[
\text{Surface Area} = 4\pi r^2
\]

where \(r\) is the radius of the sphere.

1. First, find the radius. Since the diameter is 30 inches, the radius \(r\) is:

\[
r = \frac{\text{diameter}}{2} = \frac{30}{2} = 15 \text{ inches}
\]

2. Now, substitute the radius into the surface area formula:

\[
\text{Surface Area} = 4\pi (15)^2
\]

3. Calculate \((15)^2\):

\[
(15)^2 = 225
\]

4. Now plug this back into the formula:

\[
\text{Surface Area} = 4\pi \times 225 = 900\pi
\]

So, the surface area of the sphere, in terms of \(\pi\), is:

**900π in.²**
Answered by GPT-4o mini
To find the dimensions of the cube box that can snugly fit the spherical soap, we first need to determine the radius of the sphere given its surface area. The formula for the surface area of a sphere is:

\[
\text{Surface Area} = 4\pi r^2
\]

Given that the surface area is \(63.585 \, \text{in}^2\) and using \(3.14\) for \(\pi\), we can set up the equation:

\[
63.585 = 4 \times 3.14 \times r^2
\]

Now let's solve for \(r^2\):

1. Calculate \(4 \times 3.14\):
\[
4 \times 3.14 = 12.56
\]

2. Divide both sides by \(12.56\):
\[
r^2 = \frac{63.585}{12.56} \approx 5.06
\]

3. Now, take the square root of \(r^2\) to find \(r\):
\[
r \approx \sqrt{5.06} \approx 2.25 \text{ inches}
\]

Since the diameter \(d\) of the sphere is twice the radius:

\[
d = 2r \approx 2 \times 2.25 \approx 4.5 \text{ inches}
\]

To fit a sphere snugly, the dimensions of the cube box should be equal to the diameter.

Therefore, the dimensions of the cube box should be:

**4.5 in. × 4.5 in. × 4.5 in.**