Mathematics
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
Mensuration
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Answer
Given,
Radius, r = 3 cm
Slant height be l cm
Height, h = 4 cm
By formula,
l2 = h2 + r2
⇒ l2 = 42 + 32
⇒ l2 = 16 + 9
⇒ l2 = 25
⇒ l =
⇒ l = 5 cm.
∴ Assertion (A) is false.
By formula,
Curved surface area of a cone of radius r and slant height l = πrl.
∴ Reason (R) is true.
Hence, option 2 is the correct option.
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Related Questions
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) 2856 cm3
66. The total surface area of the remaining solid is :
(b) 3388 cm3
(c) 3672 cm3
(d) 4620 cm3(a) 1870 cm2
67. The slant height of the cut out cone is :
(b) 2024 cm2
(c) 2178 cm2
(d) 2332 cm2(a) 18 cm
68. The total surface area of the cut out cone is :
(b) 25 cm
(c) 26 cm
(d) 32 cm(a) 550 cm2
(b) 704 cm2
(c) 858 cm2
(d) 616 cm2Directions:
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
70. If the given sphere is cut into two hemispheres, then how much does the total surface area get increased? (Take π = 3.14) :
(b) 5 cm
(c) 5 cm
(d) 5 cm(a) no change
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?
(b) 706.5 cm2
(c) 1015 cm2
(d) 1413 cm2(a) 135
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 :
(b) 270
(c) 405
(d) 540(a) 1350
(b) 2700
(c) 13500
(d) 27000Assertion (A) : The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is r3.
Reason (R) : For a cone of radius r and height h, volume is given by πr2h.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A) : The total surface area of a right circular cone of slant height 13 cm and radius 5 cm is 90 π cm2.
Reason (R) : Curved surface area of a right circular cone is given by πr(l + r).
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false