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

Option D.

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.