Question

The perimeter of the rectangle shown is 76 cm. it is rotated about line b.

which best describes the resulting three-dimensional figure?
•a cone with a base radius of 26cm
•a cone with a base radius of 14cm
•a cylinder with a base radius of 26cm
•a cylinder with a base radius of 14cm

Answer 1

If a rectangle is rotated about the line b, then the three-dimensional figure formed is cylinder with a circle base.

One side of the rectangle has lenght of 24 cm. Let the second side has length of x cm. The perimeter of the rectangle is 76 cm, then

24 + x + 24 + x = 76,

2x + 48 = 76,

2x= 76 - 48,

2x= 28,

x = 14 cm.

Then the three-dimensional figure is a cylinder with a base radius of 14 cm.

Answer: correct choice is D

Answer 2

Answer: •a cylinder with a base radius of 14cm

Explanation:

From the given picture it can be seen that the side of rectangle is adjacent to line B is the longer side.

If the rectangle is rotated about line b, then it will create a cylinder such that

the radius of the cylinder= smaller(width) side of the rectangle

The measure of the longer side (length) of rectangle= 24 cm

Perimeter of rectangle=
`2[length+width]`

`\\\Rightarrow\ 76=2[24+w]\\\Rightarrow\ 24+w=38\\\Rightarrow\ w=14`

hence, the measure of smaller side is 14 cm.

Therefore, the base radius =14 cm