Question

The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

Answer 1

To find the surface area of the sphere, we first need to find the value of the radius. We can do this by solving the equation πr² = 46. Once we have the radius, we can use the formula 4πr² to calculate the surface area.

Step-by-step explanation:

To find the surface area of a sphere, we need to know the radius. However, in this question, we are given the area of a cross section through the center of the sphere. Let's assume that the radius of the sphere is 'r' inches. We know that the area of a cross section through the center of a sphere is πr². So, for this question, we are given that πr² = 46 square inches. We can solve this equation to find the value of 'r'. Once we have 'r', we can use the formula for the surface area of a sphere, which is 4πr², to find the surface area of the sphere.

First, let's solve the equation πr² = 46 to find 'r':

r² = 46 / π

r² = 14.611

r ≈ 3.826

Now that we have the value of 'r', we can find the surface area of the sphere using the formula 4πr²:

Surface area = 4π(3.826)² ≈ 183.55 square inches

Answer 2

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

`A_(circle) = \pi r^2`

`\pi r^2 = 46`

`r^2 = (46)/(\pi)`

`r = \sqrt{(46)/(\pi)}`

`r = 3.83 ~in.`

surface area of sphere

`SA = 4 \pi r^2`

`SA = 4 * \pi * (3.83)^2`

`SA = 184~in.^2`