Question

The equilateral triangle shown is rotated about line a. Each

side of the triangle measures 20 mm.
What shape is created by the rotation and what is the
approximate circumference of the base?

Circumference of a circle: C = 2pi*r

a cylinder with a circumference of about 63 mm

a cylinder with a circumference of about 126 mm

a cone with a base circumference of about 63 mm

a cone with a base circumference of about 126 mm​

Answer 1

C. a cone with a base circumference of about 63 mm.

Explanation:

Rotation of a given object about a line is a process of transformation. The simple rule used here is:

(x, y) → (-y, x)

When a triangle is rotated about the given line a, this would result to a cone. Thus a 2 dimensional figure is been converted to a 3 dimensional figure.

The cone would have a circular base of radius = 10mm, since each side of the triangle measures 20mm.

The circumference of the circular base of the cone = 2
`\pi`r

= 2 ×
`(22)/(7)` × 10 (take
`\pi` =
`(22)/(7)`)

= 62.857 mm

The circumference of the base of the cone ≅ 63 mm.

Answer 2

`C \approx 62.832\,mm`

Explanation:

The rotation creates a cone and the measure of the base circumference is given by the following expression:

`C = \pi \cdot D`

Where D is the diameter.

`C = \pi \cdot (20\,mm)`

`C \approx 62.832\,mm`