Q: A Rectangular piece of paper 11 cm \times 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

Given a Rectangular piece of paper 11 cm\times 4 cm is folded without overlapping to make a cylinder of height 4 cmThe length of the paper becomes the circumference of the base of the cylinder and width becomes height.Let radius of the cylinder = r and height = h Circumference of the base of cylinder =2 \pi r = 11 cm \Rightarrow 2 \times \dfrac{22}{7} \times r = 11 \therefore r = \dfrac{7}{4} cm Now h = 4 cm Volume of the cylinder (V) = \pi r^2 h = \dfrac{22}{7} \times \dfrac{7}{4} \times \dfrac{7}{4} \times 4 cm^3 = 38.5 cm^3

Q: The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre ?

Volume of a barrel = \dfrac{22}{7} \times 0.25 \times 0.25 \times 7 = 1.375 cm^{3} Volume of ink in the bottle = \dfrac{1}{5} litre = \dfrac{1000}{5}=200 cm^{3} Therefore, total number of barrels that can be filled from the given volume of ink = \dfrac{200}{1.375} So, required number of words = \dfrac{200}{1.375}\times 330 = 48000

Q: A village, having a population of 4000 , requires 150 litres of water per head per day. It has a tank measuring 20 m \times 15 m \times 6 m. For how many days will the water of this tank last?

Given: \Rightarrow l\times b\times h=20\times 15\times 6 \Rightarrow Capacity of tank =l\times b\times h=(20\times 15\times 6) m ^{3} =1800 m ^{3} =1800000 litre \Rightarrow Consumption of water in 1 day =4000\times 150 litres =600000 litres \Rightarrow Water of this tank will last for =\cfrac{1800000}{600000} =3 days

Q: The internal measures of a cuboidal room are 12m\times 8m\times 4m. Find the total cost of whitewashing all four walls of a room, if the cost of white washing is 5 per { m }^{ 2 }. What will be the cost of white washing if the ceiling of the room is also whitewashed.

The dimensions of room is 12\times 8\times 4 The Lateral surface area is 2h(l+b) 2(4)(12+8) 8\times 20=160m^2 Cost of white wash is 5m^2 Total cost is 5\times 160=800Rs,

Question 1

A Rectangular piece of paper 11 cm  	imes  4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

Accepted Answer

Given a Rectangular piece of paper  11 cm	imes 4 cm  is folded without overlapping to make a cylinder of height 4 cmThe length of the paper becomes the circumference of the base of the cylinder and width becomes height.Let radius of the cylinder  = r  and height  = h Circumference of the base of cylinder  =2 \pi r = 11 cm \Rightarrow 2 	imes \dfrac{22}{7} 	imes r = 11 	herefore r = \dfrac{7}{4} cm  Now  h = 4 cm Volume of the cylinder  (V) = \pi r^2 h = \dfrac{22}{7} 	imes \dfrac{7}{4} 	imes \dfrac{7}{4} 	imes 4 cm^3 = 38.5 cm^3

Question 2

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm (see Fig. 13.11). Find its(i) inner curved surface area,(ii) outer curved surface area,(iii) total surface area.

Accepted Answer

(i) inner curved surface areaAccording to the question inner diameter is 4 cm,then,Inner radius of a cylindrical pipe   = {r_1} = \dfrac{{innner\,diameter}}{2} = \left( {\dfrac{4}{2}} ight)cm = 2cm Height (h) of cylindrical pipe=77 cm,Curved Surface Area of inner surface of pipe   =2\pi {r_1}h =\left( {2 	imes \dfrac{{22}}{7} 	imes 2 	imes 77} ight)c{m^2} =968\,c{m^2} (ii) Outer curved surface areaAccording to the question outer diameter is 4.4 cmOuter radius of cylindrical pipe   = {r_2} = \dfrac{{outer\,diamterer}}{2} = \left( {\dfrac{{4.4}}{2}} ight)\,cm\, = \,2.2\,cm Height of cylinder = h = 77 cm,Curved area of outer surface of pipe =  2\pi {r_2}h =\left( {2 	imes \dfrac{{22}}{7} 	imes 2.2 	imes 77} ight)c{m^2} =\left( {2 	imes 22 	imes 2.2 	imes 11} ight)\,c{m^2} =1064.8\,c{m^2} (iii) Total surface areaTotal surface area = curved surface area of inner cylinder + curved surface of outer cylinder + 2   	imes   Area of baseArea of base = area of circle with radius 2.2 cm - Area of circle with radius 2 cm =\pi {r_2}^2 - \,\pi {r_1}^2 =\dfrac{{22}}{7} 	imes ({(2.2)^2} - {(2)^2}) =\dfrac{{22}}{7} 	imes (4.84 - 4) =\dfrac{{22}}{7} 	imes (0.84) =2.74\,c{m^2} Total surface area = curved surface area of inner cylinder + curved surface area of outer cylinder + 2   	imes   Area of base  = \,968\,+ \,1064.8\,+\,2\, 	imes \,2.74 =  2032.8 + 5.76  = 2039.08\,c{m^2} Therefore, the total surface area of the cylindrical pipe is   = 2039.08\,c{m^2}

Question 3

The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

Accepted Answer

Let  d_{1}  and  d_{2}  be the two diagonals of a rhombus.Then,  d_{1}=7.5  cm and  d_{2}=12  cmWe know that,Area of Rhombus  =\dfrac{d_{1}d_{2}}{2}   =\dfrac{(7.5)(12)}{2}=45 cm^2 Hence, the answer is  45 cm^{2} .

Question 4

If two cubes of dimensions 2 cm by 2 cm by 2 cm are placed side by side, what would the dimensions of the resulting cuboid ?

Accepted Answer

The side of cube is  2cm The resultant length of cuboid is  2+2=4cm The breadth of cuboid is  2cm The height of cuboid is  2cm

Question 5

The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre ?

Accepted Answer

Volume of a barrel =  \dfrac{22}{7} 	imes 0.25 	imes 0.25 	imes 7 = 1.375   cm^{3} Volume of ink in the bottle =  \dfrac{1}{5}  litre =  \dfrac{1000}{5}=200   cm^{3} Therefore, total number of barrels that can be filled from the given volume of ink =  \dfrac{200}{1.375} So, required number of words =  \dfrac{200}{1.375}	imes 330 = 48000

Question 6

Find the area of four walls of a room having length, breadth and height as  8  m,  5  m and  3  m respectively. Find the cost of white-washing the walls at the rate of Rs.  15 / m^2 .

Accepted Answer

It is given that length, breadth and height of a room are  8  m,  5  m and  3  m respectively.Area of four walls of the room is:  2h(l + b) A=2h(l + b)=2	imes 3(8+5)=6	imes 13=78  m ^2 Area of the ceiling is:  A=l	imes b=8	imes 5=40  m ^2 Total area of the four walls and the ceiling of the room is  78+40=118  m ^2 It is given that cost of white washing is Rs. 15 /m ^2 , therefore,Total cost of white washing is: 118	imes 15=1770 Hence, the cost of white washing the walls is Rs. 1770 .

Question 7

A village, having a population of  4000 , requires  150  litres of water per head per day. It has a tank measuring  20  m  	imes 15  m  	imes 6  m. For how many days will the water of this tank last?

Accepted Answer

Given: \Rightarrow l	imes b	imes h=20	imes 15	imes 6 \Rightarrow Capacity of tank  =l	imes b	imes h=(20	imes 15	imes 6) m ^{3} =1800 m ^{3} =1800000  litre \Rightarrow Consumption of water in  1  day  =4000	imes 150  litres =600000  litres \Rightarrow Water of this tank will last for  =\cfrac{1800000}{600000} =3  days

Question 8

A cylinder has radius  7 cm and height  10 cm.Find the total surface area of the cylinder.

Accepted Answer

Given: Radius =7 cm,Height =10 cmTotal surface area =2\pi r\left(h+right) sq.units =2	imes\dfrac{22}{7}	imes 7\left(10+7ight) =44	imes 17=748 sq.cm

Question 9

The area of trapezium shaped field is  480\: m^2 , the distance between two parallel sides is  15\: cm  and one of the parallel sides is  20\: m . Find the other parallel side.

Accepted Answer

Let  ABCD  be a trapezium with parallel sides  AB  and  CD Let  AB=20  ....... (Given) and  CD=x A(\square ABCD)=480\ m^2, 	ext{height}(h)=15\ m  .......... (Given)We know that,  A(\square ABCD)=\dfrac{(AB+CD)}{2}	imes h  \implies 480 =\dfrac{20+x}{2}	imes 15 \implies \dfrac{2	imes 480}{15}=20+x \implies 64=20+x \implies x=44 Hence, length of other parallel side  CD  is  44\ m .

Question 10

The internal measures of a cuboidal room are  12m	imes 8m	imes 4m.  Find the total cost of whitewashing all four walls of a room, if the cost of white washing is 5 per  { m }^{ 2 }.  What will be the cost of white washing if the ceiling of the room is also whitewashed.

Accepted Answer

The dimensions of room is  12	imes 8	imes 4 The Lateral surface area is  2h(l+b) 2(4)(12+8) 8	imes 20=160m^2 Cost of white wash is  5m^2 Total cost is  5	imes 160=800Rs,