Question

what are the height and the diameter of the cylinder, to the nearest hundredth of a foot?

Answer 1

Given:

a.) The surface area of a cylinder is about 158.83 sq. ft.

b.) The height of the cylinder is 3 times the radius.

Let's determine the height and radius of the cylinder.

Recall the formula in getting the surface area of a cylinder:

$\text{ Surface Area = 2}\pi rh\text{ + 2}\pi\text{r}^2$

But,

h = 3r (h = height, r = radius)

Let's first find the radius:

$\text{ Surface Area = 2}\pi rh\text{ + 2}\pi\text{r}^2$$\text{ 155.83 = 2}\pi\text{\lparen r\rparen\lparen3r\rparen+ 2}\pi\text{r}^2$$\text{ 155.83 = 6}\pi r^2\text{ + 2}\pi r^2$$\text{ 8}\pi r^2\text{ = 155.83}$$\text{ }\frac{8\pi\text{r}^2}{8\pi}\text{ = }\frac{155.83}{8\pi}$$\text{ r}^2\text{ = 6.20}$$\text{ }\sqrt{r^2}\text{ = }\sqrt{6.20}$$\text{ r }\approx\text{ 2.49 feet}$

Therefore, the radius of the cylinder is approximately 2.49 feet.

For the height:

h = 3r = 3(2.51) = 7.47 feet

In Summary:

The radius is 2.49 feet

The height is 7.47 feet