i m not able to find the answer of these questions... can any 1 help me... Please show the working?

Question

1)If the minute hand of a big clock is 1.12 m long, find the rate at which its tip is moving in centimeters per minute.

2)Find the total area of cardboard used in making a match box, complete with the sliding portion, 4 cm long, 2.5 cm wide and 1.2 cm deep (ignore the thickness of the cardboard)

Answer 1

The tip traces a circle with a radius of 1.12m or 112cm. The circumference of a circle is 2πr so the circumference the tip travels is

2π(112) = 224π

It travels this distance in 1 hour (60 minutes).

So the speed of the tip is

224π cm / 60 min = 56π/15 cm/min ≈ 11.729 cm/min

Answer 2

1. The tip of the minute hand traces a circle. We need to find the distance traveled by the tip (the circumference).

Circumference (C) = 2 * pi * r = 2 * 3.14159 * 1.12 = 7.037 m

The tip travels a distance of 7.037m in one hour. Convert this to cm per minute:

Rate = 703.7 cm / 60 min = 11.7 cm / min

2. The area of the top piece = length x width = 4 * 2.5 = 10 cm^2. The area of the bottom piece is the same.

The area of the front piece = length x depth = 4 * 1.2 = 4.8 cm^2. The area of the back piece is the same.

The area of the right side piece = width x depth = 2.5 * 1.2 = 3 cm^2. The area of the left side is the same.

Add the areas of all six sides together:
10 + 10 + 4.8 + 4.8 + 3 + 3 = 35.6 cm^2.

Answer 3

(1) The tip moves along the circumference of the circle.
The formula we use is C = 2 * 3.14 * radius. Since the radius is 1.12 m, C = 7.0336 m = 703.36 cm (1 m = 100 cm)

It takes one hour for the minute hand to "make a circle" That is it takes 60 minutes for the tip to travel 703.36 cm

703.36 cm divided by 60 minutes = 11.722666666666666666666666666667 cm per minute

or
11.72 cm / minute

S.A for a rectangular prism is found by the following formula

SA = 2lw + 2wh + 2lh (length , width and height)
or in your case

SA = 2lw + 2wd + 2ld
= 2*4*2.5 + 2*2.5*1.2 + 2*4*1.2 =
= 20 + 6.0 + 9.6 = 35.6
35.6 square centimeters (AREA is in sq. units)

Answer 4

The speed of the tip is given by v = r ω where ω is the angular speed of the hand,

The minute hand takes 60 minutes to complete one revolution = 2 π radian.

ω = [2 π / 60] radian / minute.

r = 112 cm.

v = 112x 2 π / 60

v = 11.73cm / minute.
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If the outer box is cut and spread like a rectangle, the length will be
[2.5 + 1.2 + 2.5 +1.2] = 7.4cm.

The breadth will be = 4cm.

The area = 4 x 7.4 = 29.6 [cm]^2.

The sliding box has an area = 29.6 minus one area of 4 x 2.5

= 19.6 [cm] ^2.

There are two closing sides of total area = 2 x [2.5] x [1.2] = 6 cm^2.

Combined area = = 29.6 +19.6 + 6 = 55.2 [cm] ^2.

Answer 5

1.) RATE MEANS DISTANCE covered per unit TIME.
here, distance is circumference=704 cm
time is 60 mins
so, rate=704/60 cm/min=11.733 cm/min

2.) this can be done in 2 steps:
first, the outer cover- 4 sides. total area= 2( 4*2.5)+2(4*1.2).
a cuboid has six sides butthe cover has 2 sides open. making it 4. so. area= 29.6 sq.cm.
similar work canbe done for base. but diff sides will be consider. take a matchbox and it will help u. parctical is always a good option.

Answer 6

You are not expected to FIND the answers!
You are expected to reason them out!

1) what kind of path does any hand on a clock follow? for any hand, describe the path of its tip. If you know the length of the hand and how the tip travels, why can't you figure how far it travels? Hint: the minute hand travels 1/60th of a revolution in one minute. How far is 1/60th of a revolution?

2) have you ever seen a matchbox with a sliding middle?
What shape is each face of the box?
How many faces does the box have?
How many faces does the sliding part have?
Draw a picture; label each edge with the appropriate dimension. Figure out the size of each face. Figure out which faces are in each part and how many of each face.
Do some addition.

If I did all this for you, how much would you pay me?

Answer 7

Well, if it's 1.12 m long, it makes a circle of 2pi112), which is 703.72 cm distance. the rate it moves is 703.72 meters per hour.

703.72 m/hr ( 1 hour / 60 min) = 11.73 cm/min

Answer 8

Find the circumfrence of the clock
ie. 2*22/7*1.12

circimfrence=distance
time taken=60 sec=1 min
do speed=d/t

Answer 9

1. first just find circumpherence of clock. it would be 2pi1.12 which is 7.04. that is in meters, so just multiply by 10 to get centimeters. makes it 70.4cm. you know it takes an hour to move that far, which is 60 minutes, so it moves 70.4cm/60minutes, which is 1.17cm/min

2. surface area just means finding all the little rectangles. you know there is 2 of everything except for the top. so it would be 4x(4x1.2), 4x(2.5x1.2), and 3x(4x2.5). just multiply it all out. turns out to be 61.2.

Answer 10

r=1.12
angle traversed = 360/60=6 degrees
=6 * (pie/180)
so distance covered is
r*angle
=(1.12 * 6 * 3.14)/180
=0.11722 meters
=11.72 cm