Which of the following is true about the diameter of a sphere?(1 point)

Question

Responses

The diameter is 2.5 times the length of the radius.
The diameter is 2.5 times the length of the radius.

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

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

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

Answer 1

The correct statement about the diameter of a sphere from the options provided is:

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

Let's briefly evaluate the other statements:

1. The diameter is 2.5 times the length of the radius. - This is incorrect. The diameter is actually 2 times the length of the radius (Diameter = 2 × Radius).

2. The diameter is not a chord. - This is incorrect. The diameter is actually a special type of chord; it is the longest chord that passes through the center of the sphere (or circle).

3. The diameter is the shortest length on a sphere. - This is incorrect. The diameter is the longest straight line that can be drawn from one point on the sphere to another, passing through the center.

Therefore, the statement that the diameter of a sphere passes through the center is the only true statement among the options provided.

Answer 2

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

66.44 in.2
66.44 inches squared

1,063.08 in.2
1,063.08 inches squared

84.64 in.2

Answer 3

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. Since we are given the diameter of the basketball, we first need to find the radius.

The diameter is \( 9.2 \) inches, so the radius \( r \) is:

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

Now, we can substitute the radius into the surface area formula. Using \( \pi \approx 3.14 \):

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

Now calculate \( (4.6)^2 \):

\[ (4.6)^2 = 21.16 \]

Now substitute this value back into the surface area formula:

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

Calculating this step-by-step:

1. \( 4 \times 3.14 = 12.56 \)
2. \( 12.56 \times 21.16 \approx 266.09 \)

Rounding to the nearest hundredth, we get:

\[ \text{Surface Area} \approx 266.09 \text{ in}^2 \]

So the correct answer rounded to the nearest hundredth is 265.77 in.². However, it should be noted that the calculated surface area of approximately 266.09 doesn't directly match any provided options, but if we assume a small rounding difference, you should select the closest option:

265.77 in.² is the most suitable response based on the rounding.