Question

The diameter of a sphere measures 10.4 inches. What is the surface area of the sphere? a. 432.64π in^2

Answer 1

To calculate the surface area of a sphere with a diameter of 10.4 inches, the radius is first determined to be 5.2 inches. The surface area formula A = 4 π r² is then applied, giving a final value of 432.64π inches².

Step-by-step explanation:

The question you're asking is about the surface area of a sphere given its diameter. To calculate the surface area of a sphere, we use the formula A = 4 π r², where A represents the surface area and r represents the radius of the sphere. First, we need to find the radius of the sphere, which is half of the diameter. Since the diameter of the sphere is 10.4 inches, the radius would be 10.4 inches divided by 2, which is 5.2 inches. Next, we plug this value into the surface area formula.

A = 4 π (5.2 inches)²
= 4 π (27.04 inches²)
= 4 π (27.04)
= 432.64π inches².

Thus, the surface area of the sphere is 432.64π inches².

Answer 2

The correct answer is C)
`\(108.16 \pi \, \text{in}^2\)`.

The surface area
`(\(A\))` of a sphere is given by the formula:

`\[ A = 4 \pi r^2 \]`

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

The diameter
`(\(D\))` is related to the radius
`(\(r\))` by the equation
`\(D = 2r\)`. Therefore,
`\(r = (D)/(2)\)`.

In this case, the diameter is given as 10.4 inches. So, the radius
`(\(r\))` is:

`\[ r = (10.4)/(2) = 5.2 \, \text{inches} \]`

Now, substitute this value into the formula for the surface area:

`\[ A = 4 \pi (5.2)^2 \]`

`\[ A = 4 \pi * 27.04 \]`

`\[ A \approx 108.16 \pi \, \text{in}^2 \]`

Complete the question:

The diameter of a sphere measures 10.4 inches. What is the surface area of the sphere? A. 54.08π in^2 B. 432.64π in^2 C. 108.16π in^2 D. 216.32π in^2