Question

The surface area S of the sphere varies directly as square of radius r and = 16 when = 2. Find when = 36 ........ with proper steps and explanation.

Answer 1

Answer:

r = 3

Step-by-step explanation:

Here in this question, we are told that the surface area of the sphere varies directly as square of radius;

The first thing to do here is to assign variables;

let s be the surface area and r be the radius;

Now;

Since it is a direct proportional relationship;

s = k•r^2

where k represents the constant of proportionality.

now, let’s get k at first.

From the first part of the question, s = 16 and r = 2; Substituting this, we have

16 = k•2^2

4k = 16

k = 16/4

k = 4

Now from the second part of the question, we want to find r when s = 36

Let’s rewrite our equation;

s = k•r^2

where in this case, r = ? and s = 36

36 = 4 * r^2

4r^2 = 36

r^2 = 36/4

r^2 = 9

r = √9

r = 3

Kindly note we do not pick the negative square root value as radius cannot be negative

Answer 2

The surface area of the sphere when the radius is 5 inches is $100\pi$ and this can be determined by using the given data.

Given :

• The surface area of a sphere varies directly as the square of the radius.
• The surface  area is 36 when the radius is 3 inches.

The following steps can be used in order to determine the surface area S of the sphere:

Step 1 - According to the given data, the surface area S of the sphere varies directly as the square of the radius.

Step 2 - The mathematical expression of the above statement is:

$\rm S= k\times r^2$    --- (1)

where k is the proportionality constant.

Step 3 - Now, substitute the value of r and S in the above expression.

$\rm 36\pi=k \times 3^2$

$\rm k = 4\pi$

Step 4 - Now, substitute the value of $\rm k = 4\pi$ and r = 5 in the expression (1).

$\rm S = 4\pi \times 5^2$

$\rm S = 100\pi$

For more information, refer to the link given below:

https://brainly.com/question/1631786