1. If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface is :
A) 450cm2450cm2450cm2
B) 550cm2550cm2550cm2
C) 650cm2650cm2650cm2
D) 750cm2750cm2750cm2
Ans. B
Volume is given, we can calculate the radius from it, then by calculating slant height, we can get curved surface area.
13*p*r2*h=123213*227*r2*24=1232r2=1232*7*322*24=49r=7Now, r = 7cm and h = 24 cm l=r2+h2——v=72+242——-v=25cmCurved surface area =prl=227*7*25=550cm213*p*r2*h=123213*227*r2*24=1232r2=1232*7*322*24=49r=7Now, r = 7cm and h = 24 cm l=r2+h2——v=72+242——-v=25cmCurved surface area =prl=227*7*25=550cm213*p*r2*h=123213*227*r2*24=1232r2=1232*7*322*24=49r=7Now, r = 7cm and h = 24 cm l=r2+h2——v=72+242——-v=25cmCurved surface area =prl=227*7*25=550cm2
2. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
A) 4120 m cube
B) 4140 m cube
C) 5140 m cube
D) 5120 m cube
Ans. D
Explanation:
l = (48 – 16)m = 32 m, [because 8+8 = 16]b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m cube
= 5120 m cube.
3. The maximum length of a pencil that can he kept is a rectangular box of dimensions 8 cm x 6 cm x 2 cm, is
A) 217–v217–v217–v
B) 216–v216–v216–v
C) 226–v226–v226–v
D) 224–v224–v224–v
Ans. C
In this question we need to calculate the diagonal of cuboid,
which is =
l2+b2+h2———-v=82+62+22———-v=104—v=226–vl2+b2+h2———-v=82+62+22———-v=104—v=226–vl2+b2+h2———-v=82+62+22———-v=104—v=226–v
4. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km square. The height of mountain is :
A) 2.3 km
B) 2.4 km
C) 2.5 km
D) 2.6 km
Ans. B
Let the radius of the base be r km. Then,
pr2=1.54r2=1.54*722=0.49=0.7kmNow l=2.5 km, r = 0.7 kmh=2.52-0.72———vkm=6.25-0.49———v=5.76—-vkm=2.4kmpr2=1.54r2=1.54*722=0.49=0.7kmNow l=2.5 km, r = 0.7 kmh=2.52-0.72———vkm=6.25-0.49———v=5.76—-vkm=2.4kmpr2=1.54r2=1.54*722=0.49=0.7kmNow l=2.5 km, r = 0.7 kmh=2.52-0.72———vkm=6.25-0.49———v=5.76—-vkm=2.4km
5. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.
A) 1:4
B) 1:3
C) 1:2
D) 1:5
Ans. A
Let their radii be 2x, x and their heights be h and H resp.
Then,
Volume of cone =13pr2h13*p*(2x)2*h13*p*x2*H=>hH=14=>h:H=1:4Volume of cone =13pr2h13*p*(2x)2*h13*p*x2*H=>hH=14=>h:H=1:4Volume of cone =13pr2h13*p*(2x)2*h13*p*x2*H=>hH=14=>h:H=1:4
