#everydayquiz #20Questions
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
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"
.The angle of elevation of the top of a tower at a distance of 30 m from its foot is 45°. The height of the tower is : -
(a) 20 m
(b) 30 m
(c) 15√2 m
(d) 15/√2 m
2.If the ratio of the length of a pen to its shodow is 1 :√3 , the angle of elevation of the source of light is :-
(a) 40°
(b) 30°
(c) 60°
(d) 90°
3.A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60° to the horizontal. Find the height of the balloon from ground. Assume that there is no slack in the cable:-
(a) 173.2 m
(b) 17.35 m
(c) 123.2 m
(d) None of these
4.One flies a kike with a thread 150 metre long. If the thread of the kite makes an angle of 60° with the horizontal line, then the height of the kite from the ground (assuming the thread to be in a straight line) is:
(a) 50 metre
(b) 75√3
(c) 25√3
(d) 80 metre
5.From the top of h metres high cliff, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is : -
(a) 2 h/3
(b) h/3
(c) 2h/√3
(d) h/√3
6.The angle of elevation of top of a tree on the bank of a river from its other bank is 60° and from a point 20 m further away from this is 30°. The width of the river is :-
(a) 10 √3 m
(b) 10 m
(c) 20 m
(d) 20 √3 m
7.A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite side of the bank is 60°. When he moves 50 m away from the bank, the angle of elevation becomes 30°. The height of the tree and width of river respectively are : -
(a) 25√3 m, 25 m
(b) 25√3, 25√3 m
(c) 25, 25√3 m
(d) None of these
8.The angles of elevation of the top of a tower as observed from the bottom and top of a building of height 80 metre are 60° and 45° respectively. The distance of the base of the tower from the base of the building is: -
(a) 40 (√3-1)m
(b) 40 (3+ √3)m
(c) 40 (3- √3)m
(d) 40 (√3+1)m
9.A man on the top of a rock rising on a sea-shore observes a boat coming towards it. If it takes 20 minute for the angle of depression to change from 30° to 60°, how soon will the boat reach the shore?
(a) 20 minute
(b) 30 minute
(c) 10 minute
(d) 15 minute
10.From the top of cliff 90 metre high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is :
(a) 45 m
(b) 60 m
(c) 75 m
(d) 30 m
Answers and Solution:
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