The difference between outside and inside surface areas of a tube 28 cm long in 88 cm^2. The total s

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07 Jan 2016 Radius

The difference between outside and inside surface areas of a tube 28 cm long in 88 cm^2. The total surface area of the tube is 1254 cm^2, find the outer and inner radii of the tube.

OPtion

1) 4.75 cm, 3.25 cm
2) 3.75 cm, 2.75 cm
3) 3.75 cm, 1.25 cm
4) 6.75 cm, 3.25 cm
5) 5.75 cm, 4.25 cm
6) 5.75 cm, 3.25 cm
7) 3.75 cm, 2.25 cm
8) 3.75 cm, 3.25 cm
9) 4.75 cm, 3.25 cm
10)None of these

Solution

Let inner and outer radii be r and R respectively
Difference in curved surface areas = 2 Pi h (R-r)
Total surface area = 2 Pi (R+r)(h+R-r)
we should use difference in surfaces to get (R - r) and substitute it in total surface area formula to get R + r. Then we solve tog get R, r.
we have h = 28
Difference in surface area = 88 cm^2
Total surface area = 1254 cm^2
2 Pi h(R-r) = 88
R-r = 0.5
Aslo 2 Pi (h+R-r)(R+r) = 1254
Using (i) R + r = 7
Solving
R = 3.75 cm
r = 3.25 cm
Option 8)

Correct Option: 8 Best Solution (14)

JANARTHANAN RAM   9 years AGO

r1=outer radius,r2 =inner radius,h=28
2*pi*h*(r1-r2)=88;
r1-r2=0.5;
Total Surface Area of the tube=>
2*pi*h*(r1+r2) + 2*pi*(r1^2-r^2)=1254;
r1+r2=7;
so r1=3.75,r2=3.25;
So Option 8 is correct ans.

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Dinni   9 years AGO

2?h(R-r)=88
(R-r)=1/2
so by verifying options 8th option is correct

Like? Yes (3) | No (1)  

HEMA   9 years AGO

surface area of the tube s=2*pi(R^2-r^2)+2*pi*h(R+r)
total surface area = 2*pi*R*l + 2*pi*r*l
I got the diameter as 7.1331
The outer radii is 3.75cm and the inner radii as 3.25cm

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NIKHIL JAIN   9 years AGO

2pieh(R-r)= 88
on solving, R-r=0.5
also 2pieh(R+r)= 1254
on solving, R+r= 70125

On solving The answer comes to be option 8

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Aakash Beniwal   9 years AGO

ans is 3.75 and 3.25 as difference should be .5 and only option having the difference of radii .5

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pritam sinha   9 years AGO

total surface area =2?(R^2-r^2)+2?h(R+r)
and diff of surface area=2?h(R+r)
solve two equation we get the option 8

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Ritesh kumar   9 years AGO

surface area of tube: 2*pi*r*h
2pih(R-r)=88
R-r=0.5.....eq1
total surface area= 2*pi*R*h + 2*pi*r*h + 2*pi*(R^2-r^2)...
1254 = 2*pi*(R+r)(h+R-r).....solving this we get
R+r=7...eq2

from eq1 and eq2
R=3.75 and r=3.25

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swetha rangaraj   9 years AGO

Difference between outer and inner surface area
2*pi*h*(r1-r2)=88
r1 outer radius ,r2 inner
r1-r2 = 0.5
total surface area of tube
2*pi*h*(r1+r2) + 2*pi*(r1^2 -r2^2)=1254 from this
r1+r2 =7
to solve r1-r2 = 0.5 and r1+r2 =7
3.75 ,3.25

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Shagun Chaudhary   9 years AGO

2πh(a-b)=88
(a-b)=0.5
2π(a^2-b^2)+2πah+2πbh=1254
=>(a+b)=7
====>a=3.75cm
b=3.25cm

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Maneesh Gupta   9 years AGO

2πr(a-b)=88
(a-b)=0.5
2π(a²-b²)+2πah+2πbh=1254
a+b=7
a=3.75
b=3.25

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Saleel Kulkarni   9 years AGO

Let the outer radius of the tube be r1 , inner radius be r2 and the length of the pipe be h.
So h=28cm(given)

The total surface area of the pipe =Surface area of outer side+surface area of inner side+(Upper and lower area of the tube)

Surface area of inner/outer side = area of cylinder
Upper/lower area of the tube = Area of the outer circle- Area of the inner circle

So Total surface area of the pipe = 2*pr*r1*h+2*pi*r2*h+2(pi*r1^2-pi*r2^2)=1254
By simplifying we get,
28.5r1+28.5r2=199.58________________equation 1

Difference between the outer and inner surface:
2*pi*r1*h-2*pi*r2*h=88
By simplifing,
r1-r2=0.5002__________________________equation 2

By solving the equation 1 and equation 2 simultaneously we get.
r1=3.7514cm and
r2=3.2512cm

Option 4)

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Jamil Ahmed   9 years AGO

Total surface area of the tube = 2*Pi*(R+r)(R-r+h), where R is outer radius, r is inner radius and h is the length of the tube.

Similarly, difference between outer and inner surface areas = 2*Pi*(R-r)h
Therefore, 2*22/7(R+r)(R-r+28)=1254 and 2*22/7*(R-r)*28 = 88.

Solving, we get, R= 3.75 cm and r = 3.25 cm.

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Neelima Kongathi   9 years AGO

difference between outer surface area and inner surface area = 2*Pi*h(R-r) = 88sq.cm
= R-r = 0.5 ------------>eq1
total surface area = 2*pi*(R+r)(R-r) = 1254sq.cm
R+r = 7 ------------>eq2
solving eq1 & eq2
we get,
R = 3.75cm
sub.,R in eq1
r = 3.25cm

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Umair Aslam   9 years AGO

From the total surface area, we get the outer radius. From the difference between outer and inner surface areas, we get the equation to calculate inner radius. We plug-in the values of pi, height and outer radius in that equation to get the inner radius.

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