Class 9th
Mathematics
Chapter 13 - Surface area and volume
Formulas Needed . Give 1 example for each Formuals
Note : Don't copy, Don't spam .
Quality answer with good explanation will be Brainliest.
Answers
EXPLANATION.
Surface area and volumes.
(1) = Cuboid.
Volume of cuboid = L x B x H.
Total surface area of cuboid = 2(lb + bh + lh).
Lateral surface area of cuboid = 2(l + b)h.
Example :
If we have a cuboid whose length, breadth, and height are 15 cm , 10 cm , 20 cm respectively. then its surface area would be.
As we know that,
⇒ Length of cuboid = 15 cm.
⇒ Breadth of cuboid = 10 cm.
⇒ Height of cuboid = 20 cm.
As we know that,
Formula of :
Surface area of cuboid = 2[lb + bh + hl].
⇒ 2[15 x 10 + 10 x 20 + 20 x 15].
⇒ 2[150 + 200 + 300].
⇒ 2[650].
⇒ 1300 cm².
(2) = Cube.
Volume of cube = a³.
Total surface area of cube = 6a².
Lateral surface area of cube = 4a².
Example :
Hameed has build a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of tiles is ₹ 360 per dozen.
As we know that,
⇒ Edge of cube = 1.5 m = 150 cm.
⇒ Area of 1 faces of cube = side x side.
⇒ Area of 5 faces of cube = 5 x 150 x 150.
⇒ Square tiles of side = 25 cm.
⇒ Area of 1 tiles = side x side.
⇒ Area if 1 tiles = 25 x 25.
As we know that,
Number of tiles required = Surface area of the tank/area of each tiles.
Number of tiles required = 5 x 150 x 150/25 x 25.
Number of tiles required = 180.
As we know that,
⇒ Cost of 12 tiles = 360.
⇒ Cost of 1 tiles = 360/12.
⇒ Cost of 1 tiles = 30.
⇒ Cost of 180 tiles = 180 x 30 = ₹ 5400.
(3) = Cylinder.
Volume of right circular cylinder = πr²h.
Curved surface area of right circular cylinder = 2πrh.
Total surface area of right circular cylinder = 2πr(r + h).
Example :
Savitri had to make a model of a cylinder kaleidoscope for her science projects. she want to use chart paper to make the curved surface of the kaleidoscope. what would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius.
As we know that,
⇒ Radius of the kaleidoscope = 3.5 cm.
⇒ Height of kaleidoscope = 25 cm.
As we know that,
Formula of :
Curved surface area of right circular cylinder = 2πrh.
Put the value in the formula, we get.
⇒ 2 x (22/7) x 3.5 x 25.
⇒ 2 x 22/7 x 35/10 x 25.
⇒ 550 cm².
(4) = Cone.
Volume of right circular cone = 1/3πr²h.
Curved surface area of right circular cone = πrl.
Total surface area of right circular cone = πr(r + l).
Example :
Find the curved surface area of right circular cone whose slant height is 10 and base is 7 cm.
As we know that,
⇒ Slant height of cone = 10.
⇒ Base of the cone = 7 cm.
As we know that,
Formula of :
Curved surface area of right circular cone = πrl.
Put the value in the equation, we get.
⇒ 22/7 x 7 x 10.
⇒ 220 cm².
Example :
The height of a cone is 16 cm and its base is 12 cm. find the curved surface area and the total surface area of cone. use (π = 3.14).
As we know that,
⇒ Height of cone = 16 cm.
⇒ Base of cone = 12 cm.
As we know that,
Formula of :
⇒ Slant height = l = √h² + r².
Put the value in the equation, we get.
⇒ l = √16² + 12².
⇒ l = √256 + 144.
⇒ l = √400.
⇒ l = 20 cm.
Curved surface area of cone = πrl.
⇒ 3.14 x 12 x 20 = 753.6 cm².
Total surface area of cone = πr(r + l).
⇒ 3.14 x 12 (12 + 20).
⇒ 3.14 x 12 (32).
⇒ 3.14 x 12 x 32 = 1205.76 cm².
(5) = Sphere.
Volume of sphere = 4/3πr³.
Surface area of sphere = 4πr².
Example :
Find the surface area of sphere of radius 7 cm.
As we know that,
Radius = 7 cm.
Surface area of sphere = 4πr².
Put the value in the equation, we get.
⇒ 4 x 22/7 x 7 x 7.
⇒ 616 cm².
(6) = Hemisphere.
Volume of hemisphere = 2/3πr³.
Curved surface area of hemisphere = 2πr².
Total surface area of hemisphere = 3πr².
Example :
Find (1) = Curved surface area and (2) total surface area of hemisphere of radius 21 cm.
As we know that,
Radius = 21 cm.
Curved surface area of hemisphere = 2πr².
Put the value in the equation, we get.
⇒ 2 x 22/7 x 21 x 21.
⇒ 2772 cm².
Total surface area of hemisphere = 3πr².
Put the value in the equation, we get.
⇒ 3 x 22/7 x 21 x 21.
⇒ 4158 cm².
Answer:
Class 9th
Mathematics
Chapter 13 - Surface area and volume
all the Formulas for quick revision are given in the 2 attachments.
Hope it helps you,
Thank you!
