volume and surface area

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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.
20
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.
22
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.
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