Surface area and Volumes
Cube
Lateral Surface Area = 4 a^2
Total Surface Area = 6 a^2
Volume = a^3
Cuboid
Lateral Surface Area = 2 ( l h + b h ) = 2 ( l + b ) h
Total Surface Area = 2 ( l b + b h + h I )
Volume = l * b * h
Cylinder
Curved Surface Area = 2 ∏ r h
Total Surface Area = 2 ∏ r h + ∏ r^2
Volume = ∏ r^2 h
Cone
Curved Surface Area = ∏ r l
Total Surface Area = ∏ r l
+ ∏
r^2 = ∏
r ( r + l )
Volume = 1/3 ∏ r^2 h
Hemisphere
Curved Surface Area = 2 ∏ r^2
Total Surface Area = 2 ∏ r l + ∏ r^2 = 3 ∏ r^2
Volume = 2/3 ∏ r^3
Sphere
Surface Area = 4 ∏
r^2
Volume = 4/3 ∏ r^3
 |
| maths ncert solutions |
1. A plastic box of 15 m long 12.5 m wide and 650 cm deep is
to be made . It is to be open at top . Ignoring the thickness of plastic sheet
, determine
a). The area of sheet required for making the box.
b). The cost of sheet for it , if a sheet measuring 1 m^2
costs Rs 10 .
Sol. Given l = 15 m
b = 12.5 m h = 650 cm = 6.5 m
Area of sheet required for making plastic box = Total
surface area of box – Area of top of box
Area of sheet required for making plastic box = 2 ( l b + b
h + h l ) – l b
Area of sheet required for making plastic box = 2 ( 15 *
12.5 + 12.5 * 6.5 + 6.5 * 15 ) – 15 * 12.5
Area of sheet required for making plastic box = 2 ( 187.5 +
81.25 + 97.5 ) – 187.5
Area of sheet required for making plastic box = 2 * 366.25 –
187.5
Area of sheet required for making plastic box = 732.5 –
187.5
Area of sheet required for making plastic box = 545 m^2
Hence, area of sheet required for making plastic box is 545
m^2 .
b). Total cost of sheet = 10 * 545 = 5450 Rs
2. A plastic box of 10 m long 12.5 m wide and 650 cm deep is
to be made . It is to be open at top . Ignoring the thickness of plastic sheet
, determine
a). The area of sheet required for making the box.
b). The cost of sheet for it , if a sheet measuring 1 m^2
costs Rs 15 .
Sol. Given l = 10 m
b = 12.5 m h = 650 cm = 6.5 m
Area of sheet required for making plastic box = Total
surface area of box – Area of top of box
Area of sheet required for making plastic box = 2 ( l b + b
h + h l ) – l b
Area of sheet required for making plastic box = 2 ( 10 *
12.5 + 12.5 * 6.5 + 6.5 * 10 ) – 10 * 12.5
Area of sheet required for making plastic box = 2 ( 125 +
81.25 + 65 ) – 125
Area of sheet required for making plastic box = 2 * 271.25 –
125
Area of sheet required for making plastic box = 542.5 – 125
Area of sheet required for making plastic box = 417.5 m^2
Hence, area of sheet required for making plastic box is
417.5 m^2 .
b). Total cost of sheet = 15 * 417.5 = 6262.50 Rs
3. The length, breath and height of a room are 5000 cm, 4000
cm and 3000 cm respectively . Find the cost of white washing the walls of the room and the ceiling at the rate
of 10 Rs per m^2 .
Sol. Given l = 5000 cm = 50 m b = 4000 cm = 40 m h = 3000 cm = 30 m
Area of four walls and ceiling = Total surface area of room
– area of floor
Area of four walls and ceiling = 2 ( l b + b h + h l ) – l b
Area of four walls and ceiling = 2 ( 50 * 40 + 40 * 30 + 30
* 50 ) – 50 * 40
Area of four walls and ceiling = 2 ( 2000 + 1200 + 1500 ) –
2000
Area of four walls and ceiling = 2 * 4700 – 2000
Area of four walls and ceiling = 9400 – 2000
Area of four walls and ceiling = 7400 m^2
Therefore, Area of four walls and ceiling is 7400 m^2 .
Hence, the cost of white washing the walls of the room and
the ceiling = 10 * 7400 = Rs 74,000/-
4. The length, breath and height of a room are 2500 cm, 2000
cm and 1500 cm respectively . Find the cost of white washing the walls of the room and the ceiling at the rate
of 10 Rs per m^2 .
Sol. Given l = 2500 cm = 25 m b = 2000 cm = 20 m h = 1500 cm = 15 m
Area of four walls and ceiling = Total surface area of room
– area of floor
Area of four walls and ceiling = 2 ( l b + b h + h l ) – l b
Area of four walls and ceiling = 2 ( 25 * 20 + 20 * 15 + 15
* 25 ) – 25 * 20
Area of four walls and ceiling = 2 ( 500 + 300 + 375 ) – 500
Area of four walls and ceiling = 2 * 1175 – 500
Area of four walls and ceiling = 2350 – 500
Area of four walls and ceiling = 1850 m^2
Therefore, Area of four walls and ceiling is 1850 m^2 .
Hence, the cost of white washing the walls of the room and
the ceiling = 10 * 1850 = Rs 18,500 /-
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