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Shalini has to cut out circles of diameter 1¼ cm from an aluminum strip of dimensions 8¾ cm by 1¼ cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminum strip.

Answer:

From the question it is given that,

Diameter of the circle = Breadth of the aluminium strip 1¼ cm = 5/4 cm

Length of aluminium strip = 8¾ cm = 35/4 cm

∴The number of full circles cut from the aluminum strip = (35/4) ÷ (5/4)

= (35/4) × (4/5)

= (7/1) × (1/1)

= 7 circles

Radius of circle = (5/ (4 × 2)) = 5/8 cm

Area to be cut by one circle = πr^2

= (22/7) × (5/8)^2

= (22/7) × (25/64) cm^2

Now, area to be cut by 7 full circles = 7 × (22/7) × (25/64)

= (22 × 25)/64

= 550/64 cm^2

Area of the aluminum strip = length × breadth

= (35/4) × (5/4) cm^2

= (175/16) cm^2

∴The wastage of aluminum strip = (175/16) – (550/64)

= (700 - 550)/64

= 150/64

= 75/32 cm^2

"hello students welcome to lido homework
i'm kislee praveen your math tutor
and today in this video i'm going to
solve a math problem
so let us see what the question is so
there is a figure given here this is a
diagram
now what this diagram is about let us
read
shalini has to cut out circles
of diameter one one by four centimeter
from an aluminium
strip of dimensions eight three by four
centimeter by
one three by four centimeter so using
the first sentence we get the x
uh understanding that this is a
rectangle
this rectangle is a aluminium foil
and the length of the aluminum foil is
eight three by four centimeter
and width is one one by four centimeter
now shalini has to cut circles from this
aluminium foil okay and the diameter of
that every circle needs to be one
one by four centimeter so if you can
observe this one by
one one by four centimeter is also the
diameter
of the circle like this diameter
and this diameter is nothing but also
the width of the circle
okay width of the rectangle
is also diameter
okay or let me just not write or
it is width and
diameter both
okay so now what is the second sentence
see
it sees how many full circles can
shalini cut also calculate the wastage
of the aluminium strip so first we need
to check
how many circles can the shalini cut
okay so obviously if you divide
length by the width
those many circles the shalini can cut
right that is this width is one one by
four
so one width one one by four another one
one by four
another one one one by four across it
lens
will give you how many circles she can
cut
now why she can do that because
diameter is not just the width but this
part
also it's a circle so even this
is the diameter so from here to here
that distance is the diameter of the
circle
okay again from here to here another
diameter another diameter
so uh if 8 3 by 4 is divided by
1 1 by 4 you get number of circles that
can be number of diameters that can be
cut across the length so let us do that
okay
so number sorry just a minute
i need to erase this part and
write number of
circles
is equal to 8 3 by
4 divided by 1
1 by 4. this further equals you need to
convert it into improper fraction form
so it was a 32 plus 3 it is
35 by 4 divided by
4 ones are 4 plus 1 5 by 4 now
according to law of division you can
change it into multiplication
by finding the reciprocal of the second
number so this becomes
4 by 5. now this 4 and 4 gets cancelled
5 ones are 5 5 7's are 35
so there are seven circles that can be
cut okay so first part we have
already answered now let us answer the
second part
also calculate the wastage of the
aluminium strip
so for that you need to find the area of
this particular aluminium foil
that is length into bread because it's
rectangular minus
total area of all the seven circles
okay so whatever is left is the v stage
okay so you can first find
area of sec seven circles
area of seven circles
is equal to 7
into pi r square that is the area of 1
circle so this is 7 into
pi is nothing but 22 by 7 into what is
the radius of the circle its diameter by
2 so diameter is 5 by 4 that we clearly
saw here
so 5 by 4 by 2
so into 2 in the denominator you need to
do that 2 times because it is
r square by 4 into
2 so this 7 and this 7 will get
cancelled to 11. so further it cannot be
cancelled
so numerator 11 into 5 into 5
is 275 and denominator
is 32 so that much centimeter square is
the area of
all the seven circles put together
okay so now let me erase some part
the first question part and we can
continue solving
the second part of the question okay
so coming back to that we need to find
the
area of the aluminium foil
area of a l dot is aluminium
foil is equal to length into bread
so length is how much 5 by
4 that is the width and length is
35 by 4 so that is
equal to 175
by 16 square centimeter
so now you can easily calculate the
wastage
v stage is equal to
area of i'm writing a rectangle
minus area of 7
circles right so
let me erase some more part of it and
then continue
solving so this becomes
equal to area of rectangle is how much
it is 175
by 16 minus area of 7 circles we got it
as
275 by 32
so here the lcm of 16 and 32 is
32 so 16 2's are 32 so 175
into 2 will give you 350
minus 275 so the final answer is
75 by 32
square centimeter now you can convert it
into decimal
or mixed fraction form but this is the
final answer
i hope it's clear if you still have any
doubt put a message in the comment
section
and subscribe to our channel for regular
updates bye
"

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