Four pencils are held together with a band. the figure on the right shows the bottom end of the pencils and the band. each of the pencils has a diameter of 10mmfind the length of the band in this position. give your answer in terms of pi.

The length of the band is the number of units it covers

The actual length of the band is:

The diameter of 1 pencil is given as:

The circumference of 1 pencil is:

So, we have:

Multiply by 4, to calculate the circumference of all pencils

The rubber band covers a quarter of the 4 pencils.

So, we divide by 4

The length of the band on one pencil is:

Multiply by 4, for the 4 pencils

So, the actual length of the band is:

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(40+10π) mm.

Step-by-step explanation: Given diameter of the circle = 10mm.

Radius of the circle = 10/2 = 5 mm.

From the figure, we can see that each or the four corners makes a quarter of the circle.

And four corners would make the complete circle with radius 5mm.

Therefore, circumference of the four quarters of a circle = 2 π r

= 2 π  (5) = 10 π.

Now, we can see that each side 10 mm of band also there.

So, the length of straight band on all four sides = 4 × 10 = 40 mm.

Total length of the band = (40+10π) mm

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step-by-step explanation: