Question

The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr a cone with a base circumference of about 25 units a cone with a base circumference of about 50 units a cylinder with a circumference of about 25 units a cylinder with a circumference of about 50 units

Answer 1

The perimeter of the square is calculated through the equation,
                                        4x = P
where P is the perimeter and x is the measure of the sides.

When P is 32 units then,
                                         32 units = 4(x)
                                                 x = 8 inches

This 8 inches is the diameter of the cylinder formed by the rotation. 
The circumference of the base is calculated through,
                            C = 2πr = πD
Substituting the known values,
                              C = π(8 units) = 8π units
When π is equal to 3.14, we solve for the numerical value of the cylinder as follows,
                                      C = 8(3.14) = 25.12 units
Thus, the figure formed is a cylinder with base circumference equal to 25 units. The answer is the third choice. 

Answer 2

Answer:

Option D.

Step-by-step explanation:

Perimeter of the square = 32

Formula for perimeter of a square is

$Perimeter=4a$

where, a is the side length of square.

$32=4a$

Divide both sides by 4.

$8=a$

The side length of square is 8 units

Let as assume that the diagram of the given situation is shown below.

If the square is rotated about line k, then it will form a cylinder with radius 8 units.

Circumference of a circle = 2πr

where, r is the radius of the circle.

Circumference of the base is

$C=2\pi (8)$

$C=16\pi$

$C=50.26548$

$C\approx 50$

The shape is created by the rotation is a cylinder with a circumference of about 50 units.

Therefore, the correct option is D.