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Sara is a drummer in her school is marching band she wants to make a geometrically similar model of a snare drum for her stuffed animals. To find the dimensions she should use to make a cylindrical model with a scale of 1 : 4, Sara measures the radius and height of a snare drum and multiplies each dimension by 1/2. Which statement is true?

A. A cylinder with Sara’s dimensions will be geometrically similar, and the scale factor will be 1:4


B. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:2


C. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:8


D. A cylinder with Sara’s dimensions will not be geometrically similar

Respuesta :

Answer:

Option B.

Step-by-step explanation:

Let the radius of the snare drum = r

and radius of the model = R

Ratio of the dimensions of the snare drum and the model = 1 : 4

So, [tex]\frac{r}{R}=\frac{1}{4}[/tex]

Now as per question, dimensions of the snare drum is multiplied by a scale factor of [tex]\frac{1}{2}[/tex]

Radius of the snare drum = [tex]\frac{r}{2}[/tex]

Ratio of the radius of the snare drum and cylindrical model ,

[tex]\frac{\frac{r}{2}}{R} =\frac{1}{4}[/tex]

[tex]\frac{r}{2R}=\frac{1}{4}[/tex]

[tex]\frac{r}{R}=\frac{1}{2}[/tex]

Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2

Option B is the answer.