Question

Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone.

Dimensions of the conical part of a silo is as follows:

Radius of base = 1.5 m

Height = 2 m

Dimensions of the cylindrical part of a silo is as follows:

Radius = 1.5 m

Height = 7 m

On the basis of the above information answer the following questions.

(i) Calculate the slant height of the conical part of one silo.

(ii) Find the curved surface area of the conical part of one silo.

(iii) (A) Find the cost of metal sheet used to make the curved cylindrical part of 1 silo at the rate of ₹2000 per m2 .

 OR

(iii) (B) Find the total capacity of one silo to store grains

Answer 1

l= √r² + h² 

 = √(1.5)² + (2)² 

 = √2.25 + 4 

 = √6.25 

 = 2.5 m 

(ii) CSA of cone = πrl 

 = 22/7 x 1.5 x 2.5 

 = 11.78 m² 

 CSA of cylinder = 2πrh 

 = 2 x 22 7 x 1.5 x 7 

 = 66 m² 

 Cost of metal sheet used = 66 x 2000 = ₹1,32,000 

 OR 

Volume of cylinder = πr²h 

= 22/7 x (1.5)² x 7 

= 49.5 m³

Volume of cone = 1/3πr²h 

 = 1/3 x 22/7 x (1.5)² x 2 

 = 4.71 m³ 

Total capacity = 49.5 + 4.71 = 54.21 m³