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Surface Areas and Volumes Ex-13.5 Interview Questions Answers

Question 1 :

A copper wire, 3 mmin diameter, is wound about a cylinder whose length is 12 cm, and diameter 10cm, so as to cover the curved surface of the cylinder. 

Answer 1 : Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm_3.

Question 2 :

A right trianglewhose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve aboutits hypotenuse. Find the volume and surface area of the double cone so formed.(Choose value of π as found appropriate)

Answer 2 :

Question 3 :

A cistern,internally measuring 150 cm × 120 cm × 100 cm, has 129600 cm3 ofwater in it. Porous bricks are placed in the water

Answer 3 :  until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each being 22.5 cm × 7.5 cm × 6.5 cm?


Solution:

Given that the dimension of the cistern = 150× 120 × 110

So, volume = 1980000 cm3

Volume to be filled in cistern = 1980000 –129600

= 1850400 cm3

Now, let the number of bricks placed be “n”

So, volume of n bricks will be =n×22.5×7.5×6.5

Now as each brick absorbs one-seventeenth ofits volume, the volume will be

= n/(17)×(22.5×7.5×6.5)

For the condition given in the question,

The volume of n bricks has to be equal tovolume absorbed by n bricks + Volume to be filled in cistern

Or, n×22.5×7.5×6.5 =1850400+n/(17)×(22.5×7.5×6.5)

Solving this we get,

n = 1792.41

Question 4 :

In one fortnight ofa given month, there was a rainfall of 10 cm in a river valley. If the area ofthe valley is 97280 km2

Answer 4 : show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Solution:

From the question, it is clear that

Total volume of 3 rivers = 3×[(Surface area ofa river)×Depth]

Given,

Surface area of a river = [1072×(75/1000)] km

And,

Depth = (3/1000) km

Now, volume of 3 rivers =3×[1072×(75/1000)]×(3/1000)

= 0.72 km3

Now, volume of rainfall = total surface area ×total height of rain

= 9.7 km3

For the total rainfall was approximatelyequivalent to the addition to the normal water of three rivers, the volume ofrainfall has to be equal to volume of 3 rivers.

But, 9.7 km3 ≠ 0.72 km3

So, the question statement is false.

Question 5 :

An oil funnel madeof tin sheet consists of a 10 cm long cylindrical portion attached to a frustumof a cone. If the total height is 22 cm,

Answer 5 :  diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see Fig.).


Selected

 

Surface Areas and Volumes Ex-13.5 Contributors

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