You look at a button under a magnifying glass. Find the actual length of the button.

Question

The image of the button is 6 times the​ button's actual size and has a diameter of 21 cm.
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Part 1
The​ button's actual diameter is
  
enter your response here cm.
​(Type an integer or a​ decimal.)

Answer 1

To find the actual diameter of the button, we can use the fact that the image is 6 times the actual size of the button.

Given:

• Diameter of the image = 21 cm
• Magnification = 6 (The image is 6 times larger than the actual size)

We can find the actual diameter of the button (let's call it \( d \)) using the formula:

\[ \text{Diameter of the image} = \text{Magnification} \times \text{Actual diameter} \]

So, we have:

\[ 21 , \text{cm} = 6 \times d \]

Now, solve for \( d \):

\[ d = \frac{21 , \text{cm}}{6} = 3.5 , \text{cm} \]

Thus, the actual diameter of the button is 3.5 cm.