Mathematics
Directions: The surface area of a solid metallic sphere is 900 π cm2. Based on this information, answer the following questions: 69. If the given sphere is melted and recast into 3 smaller spheres of equal volumes, then the radius of each smaller sphere is : (a) 5 cm (b) 5 cm (c) 5 cm (d) 5 cm 70. If the given sphere is cut into two hemispheres, then how much does the total surface area get increased? (Take π = 3.14) : (a) no change (b) 706.5 cm2 (c) 1015 cm2 (d) 1413 cm2 71. If the given sphere is melted and recast into solid right cones, each of radius 2.5 cm and height 8 cm, how many cones are formed? (a) 135 (b) 270 (c) 405 (d) 540 72. If the given sphere is melted and recast into small spheres each of radius 0.5 cm, then the number of spheres formed is : (a) 1350 (b) 2700 (c) 13500 (d) 27000
Related Questions
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
62. The cost of cloth required to make each tent at the rate of ₹ 80 per square meter is :
(b) 17.5 m
(c) 18.5 m
(d) 19.5 m(a) ₹ 76560
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?
(b) ₹ 80140
(c) ₹ 82720
(d) ₹ 85960(a) 960
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?
(b) 1155
(c) 1320
(d) 1440(a) 48 m3
(b) 52 m3
(c) 55 m3
(d) 77 m3Directions:
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) 2856 cm3
(b) 3388 cm3
(c) 3672 cm3
(d) 4620 cm3
(a) 1870 cm2
(b) 2024 cm2
(c) 2178 cm2
(d) 2332 cm2
(a) 18 cm
(b) 25 cm
(c) 26 cm
(d) 32 cm
(a) 550 cm2
(b) 704 cm2
(c) 858 cm2
(d) 616 cm2
Assertion (A) : Slant height of a cone of height 4 cm and radius 3 cm is (4 + 3) cm = 7 cm.
Reason (R) : Curved surface area of a cone of radius r and slant height l is πrl.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false