1.If S is the total surface area of a cube and V is its volume, then which one of the following is correct?
(a) V^3= 216 S^2
(b) S^3= 216 V^2
(c) S^3= 6 V^2
(d) S^2= 36 V^3
2.The curved surface of a cylinder is 1000 sq cm. A wire of a diameter 5 mm is wound around it, so as to cover it completely. What is the length of the wire used?
(a) 22 m
(b) 20 m
(c) 18 m
(d) None of these
3.The volume of a cone is equal to that of a sphere. If the diameter of base of cone is equal to the diameter of the sphere, what is the ratio of height of cone to the diameter of the sphere?
(a) 2 : 1
(b) 1 : 2
(c) 3 : 1
(d) 4 : 1
4.The volume of a sphere is 8 times that of another sphere. What is the ratio of their surface areas?
(a) 8 : 1
(b) 4 : 1
(c) 2 : 1
(d) 4 : 3
5.How many litres of water flow out of a pipe having an area of cross-section of 5 cm^2 in one minute, if the speed of water in the pipe is 30 cm/s?
(a) 90 L
(b) 15 L
(c) 9 L
(d) 1.5 L
6.A cylindrical rod of length h is method and cast into a cone of base radius twice that of the cylinder. What is the height of the cone?
(a) 3h/4
(b) 4h/3
(c) 2h
(d) h/2
7.If C1 is right circular cone with base radius r1 cm and height h1 cm and C2 is a right circular cylinder with base radius r2 cm and height h2 cm and if r1 : r2 = 1 : n (where n is a positive integer) and their volumes are equal, then which one of the following is correct?
(a) h1 = 3nh2
(b) h1 = 3n^2 h2
(c) h1 = 3h2
(d) h1 = n^2h2
8.In which one of the following pairs does the first number represent the perimeter of one face of a cube and the second number represent the volume of the cube?
(a) (16, 32)
(b) (20, 125)
(c) (32, 16)
(d) (125, 20)
9.A unit radian is approximately equal to :
(a) 57° 17’ 43”
(b) 57° 17’ 45”
(c) 57° 16’ 22”
(d) 57° 17’ 49”
10.Assume the Earth to be a sphere of radius R. When is the radius of the circle of latitude 40° S ?
(a) R cos 40°
(b) R sin 80°
(c) R sin 40°
(d) R tan 40°
SOLUTION
1.(b); Surface area of cube (S) = 6a^2
Volume of cube (V) = a^3
S^3 = 216 a^6
=> V^2 = a^6
S^3 = 216 V^2
2.(b)
3.(a); Volume of cone = Volume of sphere
1/3 πr^2 h = 4/3 πr^3
h = 4r => h/2r=2/1
4.(b) ; According to question,
4/3 π(r1)^3 = 8 × 4/3 π(r2)^3
(r1)^3/(r2)^3 =8 => r1/r2 = 2/1
Required ratio =(4π〖r1〗^2)/(4π〖r2〗^2 )= 〖(2/1)〗^(2 ) = 4/1
5.(c); Height of water in a second = 30 cm
Height of water in 60 second = 30 * 60
h = 1800 cm
Area of cross section = πr^2=5sq cm
Volume of water flow in one minute = πr^2 h
= 5 * 1800 = 9000 cu cm = 9000/1000 It = 9 lt
6.(a) ; Let the radius of cylinder be r and radius of cone be R
R = 2r
According to question,
Volume of cylinder = Volume of cone
πr^2 h=1/3 πR^2 H
r^2 h=1/3 π(2r)^2 H
H = 3h/4
7.(b)
8.(b) ; From option (b)
Let permeter 4a = 20
=> a = 5
Volume of cube = a^3 = 5^3 = 125
9.(c); 1 Radian = 180/π degree
= (180 ×7)/22 =57 3/11=57°(3/11 ×60)
= 57°16' (4/11 ×60)" = 57°11' 21.8"
= 57°16' 22"
10.(a).
1.(b); Surface area of cube (S) = 6a^2
Volume of cube (V) = a^3
S^3 = 216 a^6
=> V^2 = a^6
S^3 = 216 V^2
2.(b)
3.(a); Volume of cone = Volume of sphere
1/3 πr^2 h = 4/3 πr^3
h = 4r => h/2r=2/1
4.(b) ; According to question,
4/3 π(r1)^3 = 8 × 4/3 π(r2)^3
(r1)^3/(r2)^3 =8 => r1/r2 = 2/1
Required ratio =(4π〖r1〗^2)/(4π〖r2〗^2 )= 〖(2/1)〗^(2 ) = 4/1
5.(c); Height of water in a second = 30 cm
Height of water in 60 second = 30 * 60
h = 1800 cm
Area of cross section = πr^2=5sq cm
Volume of water flow in one minute = πr^2 h
= 5 * 1800 = 9000 cu cm = 9000/1000 It = 9 lt
6.(a) ; Let the radius of cylinder be r and radius of cone be R
R = 2r
According to question,
Volume of cylinder = Volume of cone
πr^2 h=1/3 πR^2 H
r^2 h=1/3 π(2r)^2 H
H = 3h/4
7.(b)
8.(b) ; From option (b)
Let permeter 4a = 20
=> a = 5
Volume of cube = a^3 = 5^3 = 125
9.(c); 1 Radian = 180/π degree
= (180 ×7)/22 =57 3/11=57°(3/11 ×60)
= 57°16' (4/11 ×60)" = 57°11' 21.8"
= 57°16' 22"
10.(a).
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