Surface Areas and Volumes Ex 13.5 Solutions
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 = 1792.41In 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.
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.).