1. The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:
A) 79.8cm379.8cm379.8cm3
B) 79.4cm379.4cm379.4cm3
C) 89.8cm389.8cm389.8cm3
D) 89.4cm389.4cm389.4cm3
Ans. C
Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm
Volume of cone =13pr2h=13*227*3.5*3.5*7=269.53cm3=89.8cm3Volume of cone =13pr2h=13*227*3.5*3.5*7=269.53cm3=89.8cm3Volume of cone =13pr2h=13*227*3.5*3.5*7=269.53cm3=89.8cm3
(radius is taken as 3.5, as diameter is 7 cm)
2. A hollow spherical metallic ball has an external diameter 6 cm and is 1/2 cm thick. The volume of metal used in the metal is:
A) 4715cm34715cm34715cm3
B) 4735cm34735cm34735cm3
C) 4775cm34775cm34775cm3
D) 4795cm34795cm34795cm3
Ans. B
If we are given with external radius and thickness, we can get the internal radius by subtracting them. Then the volume of metal can be obtained by its formula as,
External radius = 3 cm,
Internal radius = (3-0.5) cm = 2.5 cm
Volume of sphere =43pr3=43*227*[32-2.52]cm3=43*227*918cm3=1433cm3=4723cm3Volume of sphere =43pr3=43*227*[32-2.52]cm3=43*227*918cm3=1433cm3=4723cm3Volume of sphere =43pr3=43*227*[32-2.52]cm3=43*227*918cm3=1433cm3=4723cm3
3. The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:
A) 4 cm
B) 6 cm
C) 8 cm
D) 10 cm
Ans. B
Curved surface area of sphere =4pr2Surface area of cylinder =2prh=>4pr2=2prh=>r2=6*122=>r2=36=>r=6Curved surface area of sphere =4pr2Surface area of cylinder =2prh=>4pr2=2prh=>r2=6*122=>r2=36=>r=6Curved surface area of sphere =4pr2Surface area of cylinder =2prh=>4pr2=2prh=>r2=6*122=>r2=36=>r=6
Note: Diameter of cylinder is 12 so radius is taken as 6. View Answer Comment
4. 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.
A) 4 cm
B) 6 cm
C) 8 cm
D) 10 cm
Ans. A
In this type of question, just equate the two volumes to get the answer as,
Volume of cylinder =pr2hVolume of sphere =43pr3=>12*43pr3=pr2h=>12*43pr3=p*8*8*2=>r3=8*8*2*312*4=>r3=8=>r=2cm=>Diameter =2*2=4cmVolume of cylinder =pr2hVolume of sphere =43pr3=>12*43pr3=pr2h=>12*43pr3=p*8*8*2=>r3=8*8*2*312*4=>r3=8=>r=2cm=>Diameter =2*2=4cmVolume of cylinder =pr2hVolume of sphere =43pr3=>12*43pr3=pr2h=>12*43pr3=p*8*8*2=>r3=8*8*2*312*4=>r3=8=>r=2cm=>Diameter =2*2=4cm View Answer
5. A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
A) 45%
B) 56%
C) 67%
D) 75%
Ans. D
We will first subtract the cone volume from wood volume to get the wood wasted.
Then we can calculate its percentage.
Sphere Volume =43pr3Cone Volume =13pr2hVolume of wood wasted =(43p*9*9*9)-(13p*9*9*9)=p*9*9*9cm3Required Percentage =p*9*9*943p*9*9*9*100%=34*100%=75%Sphere Volume =43pr3Cone Volume =13pr2hVolume of wood wasted =(43p*9*9*9)-(13p*9*9*9)=p*9*9*9cm3Required Percentage =p*9*9*943p*9*9*9*100%=34*100%=75%Sphere Volume =43pr3Cone Volume =13pr2hVolume of wood wasted =(43p*9*9*9)-(13p*9*9*9)=p*9*9*9cm3Required Percentage =p*9*9*943p*9*9*9*100%=34*100%=75%
6. A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface will be :
A) 2:12:12:1
B) 1:2v1:2v1:2v
C) 2v:12v:12v:1
D) 3v:13v:13v:1
Ans. C
Let the radius of hemisphere and cone be R,
Height of hemisphere H = R.
So the height of the cone = height of the hemisphere = R
Slant height of the cone
=R2+R2——-v=2vRHemisphere Curved surface areaCone Curved surface area=2pR2p*R*2vR=2v:1=R2+R2——-v=2vRHemisphere Curved surface areaCone Curved surface area=2pR2p*R*2vR=2v:1=R2+R2——-v=2vRHemisphere Curved surface areaCone Curved surface area=2pR2p*R*2vR=2v:1
