1. Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
A) 3v:13v:13v:1
B) 7v:17v:17v:1
C) 2v:12v:12v:1
D) 2:12:12:1
Ans. C
Let their heights be h and 2h and radii be r and R respectively then.
pr2h=pR2(2h)=>r2R2=2hh=21=>rR=2v1=>r:R=2v:1pr2h=pR2(2h)=>r2R2=2hh=21=>rR=2v1=>r:R=2v:1pr2h=pR2(2h)=>r2R2=2hh=21=>rR=2v1=>r:R=2v:1
2. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by:
A) 1137cm1137cm1137cm
B) 1127cm1127cm1127cm
C) 1117cm1117cm1117cm
D) 11cm11cm11cm
Ans. A
Let the drop in the water level be h cm, then,
Volume of cylinder= pr2h=>227*352*352*h=11000=>h=11000*7*422*35*35cm=807cm=1137cmVolume of cylinder= pr2h=>227*352*352*h=11000=>h=11000*7*422*35*35cm=807cm=1137cmVolume of cylinder= pr2h=>227*352*352*h=11000=>h=11000*7*422*35*35cm=807cm=1137cm
3. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will be:
A) 76 m
B) 80 m
C) 84 m
D) 88 m
Ans. C
Let the length of the wire be h
Radius=12mm=120cmpr2h=66227*120*120*h=66=>h=66*20*20*722=8400cm=84mRadius=12mm=120cmpr2h=66227*120*120*h=66=>h=66*20*20*722=8400cm=84mRadius=12mm=120cmpr2h=66227*120*120*h=66=>h=66*20*20*722=8400cm=84m
4. A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8g/cm cube, then find the weight of the pipe.
A) 3.696 kg
B) 3.686 kg
C) 2.696 kg
D) 2.686 kg
Ans. A
External radius = 4 cm
Internal radius = 3 cm [because thickness of pipe is 1 cm]Volume of iron =pr2h=227*[42-32]*21cm3=227*1*21cm3=462cm3Volume of iron =pr2h=227*[42-32]*21cm3=227*1*21cm3=462cm3Volume of iron =pr2h=227*[42-32]*21cm3=227*1*21cm3=462cm3
Weight of iron = 462*8 = 3696 gm
= 3.696 kg
5. The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is:
A) 116pcm2116pcm2116pcm2
B) 122pcm2122pcm2122pcm2
C) 124pcm2124pcm2124pcm2
D) 136pcm2136pcm2136pcm2
Ans. D
Curved surface area of cone=prll=r2+h2——vl=82+152——-v=17cmCurved surface area =prl=p*8*17=136pcm2Curved surface area of cone=prll=r2+h2——vl=82+152——-v=17cmCurved surface area =prl=p*8*17=136pcm2Curved surface area of cone=prll=r2+h2——vl=82+152——-v=17cmCurved surface area =prl=p*8*17=136pcm2
