Question

The area of the front face of the analog clock shown below is 153.86 square inches. The length of the minute hand is 0.2 inches less than the radius of the front face.

What is the length of the arc, rounded to the nearest hundredth of an inch, the minute hand makes when it moves from the number 8 to the number 2 on the clock?

Answer 1

@AravindG

Answer 2

@AravindG

Answer 3

Huh?

Answer 4

in this question we have 2 circles
1. the face of the clock
2. the circle the tip of the minute hand makes

first we need to find the radis of the inner circle (the length of the minute hand)

A = pi (r)^2 formula for area of a circle

153.86 = pi (r^2), now divide both sides by pi

153.86 = 3.14(r^2)
------ ------
3.14 3.14

49 = r^2

7 = r this is the radis of the face of the clock.

7 - .2 = 6.8 is the length of the minute hand (the length of the min hand)

you with me so far?

Answer 5

Okay so the length of the arc is 6.8?

Answer 6

Sorry mistaken thought area was the radius . Go with the explanation by @Jim766

Answer 7

no the radis of the inner circle is 6.8

now we need to find the circumference of this inner circle

C = 2 (Pi) r

C = 2(3.14) 6.8 what is the circumference of this circle?

Answer 8

42.70, so then we divide by 2? and that gives me 21.35 as the length of the arc?

Answer 9

great!

Answer 10

Thank you! I have one more question, can you help?

Answer 11

I can try...

Answer 12

Jamie made a wax model of a rolling pin of diameter 8 cm. The rolling pin was shaped like a right circular cylinder with a right circular cone at each end as shown below.

What was the total surface area of the rolling pin? Using complete sentences, describe the steps you used to calculate the surface area.

Answer 13

surface area of cylinder Surface Area = 2(pi r 2) + (2 pi r)* h

surface area of cone SA = pi(r)s + pi(r^2)

Answer 14

in this type of problem, you find the area of the cylinder, then the 2 cones and add it together
Start with the cylinder. We need radis and height
can you get those from the diagram?

Answer 15

Radius is 4, I'm not sure about height because of the two cones

Answer 16

if the cylinder was standing up, the height would be 12, do you see where I got that?

Answer 17

Yes

Answer 18

SA = 2(3.14)(16) + 2 (3.14)(4 )(12) so what is the surface area of the cylinder?

Answer 19

175.84

Answer 20

SA = 2(3.14)(16) + 2 (3.14)(4 )(12)
Sa = 100.48 + 301.44

Sa = 401.92 please check me..

Answer 21

Yeah sorry I missed the 4 in the above equation

Answer 22

now the cone

SA = 3.14(4)(5)

Answer 23

62.80

Answer 24

great, now there are 2 of them....

Answer 25

plus the area of the cylinder

Answer 26

125.60 + 401.92 =527.52

Answer 27

nice job...

make sense?

Answer 28

Kind of, not really, lol it's starting to hurt my head. So the total surface area is 527.52 cm?

Answer 29

oh yeah, the units....are cm^2

527.52 cm^2 in area, units are always squared

but that is it...

Answer 30

Okay thank you!! :)

Answer 31

I know it is a little painful....keep working at it!