Volume and Surface Area

1.

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

A. 12 cm3 B. 15 cm3 C. 16 cm3 D. 20 cm3 Answer: Option A Explanation: Clearly, we have r = 3 cm and h = 4 cm.  Volume = 1 r2h = 1 x  x 32 x 4 cm3 = 12 cm3. 3 3 2.  In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is: A. 75 cu. m B. 750 cu. m C. 7500 cu. m D. 75000 cu. m Answer: Option B Explanation: 1 hectare = 10,000 m2 So, Area = (1.5 x 10000) m2 = 15000 m2. Depth = 5 m = 1 m. 100 20  Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3. 3.  A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is: A. 720 B. 900 C. 1200 D. 1800 Answer: Option C Explanation: 2(15 + 12) x h = 2(15 x 12)  h = 180 m = 20 m. 27 3  Volume = 15 x 12 x 20 m3 = 1200 m3. 3

4.	66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
	A. 84 B. 90 C. 168 D. 336 Answer: Option A Explanation: Let the length of the wire be h. Radius = 1 mm = 1 cm. Then, 2 20 22 x 1 x 1 x h = 66. 7 20 20  h = 66 x 20 x 20 x 7 = 8400 cm = 84 m.

5.	A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
	A. 3.6 kg B. 3.696 kg C. 36 kg D. 36.9 kg Answer: Option B Explanation: External radius = 4 cm, Internal radius = 3 cm. Volume of iron = 22 x [(4)2 - (3)2] x 21 cm3 7 = 22 x 7 x 1 x 21 cm3 7 = 462 cm3.  Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg