Directions:
At an NCC camp, several tents were installed. Each tent is cylindrical to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m.
Based on this information, answer the following questions:
61. The slant height of the conical portion of the tent is :
(a) 16.5 m
(b) 17.5 m
(c) 18.5 m
(d) 19.5 m
62. The cost of cloth required to make each tent at the rate of ₹ 80 per square meter is :
(a) ₹ 76560
(b) ₹ 80140
(c) ₹ 82720
(d) ₹ 85960
63. If each cadet requires 8 m² of floor space and there are 15 tents in all how many cadets can be accommodated in the camp?
(a) 960
(b) 1155
(c) 1320
(d) 1440
64. If a tent has maximum number of cadets that it can accommodate as calculated in the above questions, what is the volume of air available to each cadet to breathe?
(a) 48 m³
(b) 52 m³
(c) 55 m³
(d) 77 m³

Question

Directions:

At an NCC camp, several tents were installed. Each tent is cylindrical to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m.

Based on this information, answer the following questions:

61. The slant height of the conical portion of the tent is :

(a) 16.5 m
(b) 17.5 m
(c) 18.5 m
(d) 19.5 m

62. The cost of cloth required to make each tent at the rate of ₹ 80 per square meter is :

(a) ₹ 76560
(b) ₹ 80140
(c) ₹ 82720
(d) ₹ 85960

63. If each cadet requires 8 m² of floor space and there are 15 tents in all how many cadets can be accommodated in the camp?

(a) 960
(b) 1155
(c) 1320
(d) 1440

64. If a tent has maximum number of cadets that it can accommodate as calculated in the above questions, what is the volume of air available to each cadet to breathe?

(a) 48 m³
(b) 52 m³
(c) 55 m³
(d) 77 m³

KnowledgeBoat · Accepted Answer

61\. Given, Height of cylinder, h = 3 m Total height of tent, T = 13.5 m Height of cone, H = T - h = 13.5 - 3 = 10.5 m Radius of base of cylinder = Radius of cone = r = 14 m Slant height of cone be l m. l2 = r2 + H2 ⇒ l2 = 142 + 10.52 ⇒ l2 = 196 + 110.25 ⇒ l2 = 306.25 ⇒ l = = 17.5 m Hence, Option (b) is the correct option. 62\. Curved surface area of tent = Curved surface area of cone + Curved surface area of cylinder = 2πrh + πrl = πr(2h + l) Given, cost of cloth required to make each tent is ₹ 80 per square meter. ⇒ Total cost = 80 × 1034 = ₹ 82720 Hence, Option (c) is the correct option. 63\. The floor space of a tent is base area of cylinder. ∴ Area of base = πr2 = × 14 × 14 = 22 × 2 × 14 = 616 m2 Given each cadet requires 8 m2 of floor space. The number of cadets per tent = = 77 cadets. Given, there are 15 tents. ∴ Total number of cadets = 77 × 15 = 1155 cadets. Hence, Option (b) is the correct option. 64\. Volume of air in each tent = Volume of air in cylinder + Volume of air in cone Volume of air available to each cadet to breathe = = 52 m3. Hence, Option (b) is the correct option.

Mathematics

Mensuration

Related Questions

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is one-fourth of its height. The surface area of the solid is :
462 cm²
693 cm²
750 cm²
770 cm²

Directions:
From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out.
Based on this information, answer the following questions:
65. The volume of the remaining solid is :

Mathematics

Mensuration

Related Questions

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is one-fourth of its height. The surface area of the solid is :462 cm2693 cm2750 cm2770 cm2

Directions:From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out.Based on this information, answer the following questions:65. The volume of the remaining solid is :

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is one-fourth of its height. The surface area of the solid is :
462 cm²
693 cm²
750 cm²
770 cm²

Directions:
From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out.
Based on this information, answer the following questions:
65. The volume of the remaining solid is :