1.50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 , then the rise in the water level in the tank will be:
A) 20 cm
B) 25 cm
C) 35 cm
D) 50 cm
2.A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A) 720
B) 900
C) 1200
D) 1800
3.The cost of the paint is rs.36.50 per kg. if 1kg of paint covers 16sq.ft, how much will it cost to paint outside of a cube having 8 feet each side
A) Rs.962
B) Rs.672
C) Rs.546
D) Rs.876
4.What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
A) 814
B) 820
C) 840
D) 844
5.Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.
A) 3:1
B) 2:1
C) 4:1
D) 5:1
6.The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
A) 16cm
B) 18cm
C) 24cm
D) .Data inadequate
7.What part of the volume of a cube is the pyramid whose base is the base of then cube and whose vertex is the center of the cube?
A) 4:1
B) 5:1
C) 6:1
D) 7:1
8.The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.
A) 50%
B) 40%
C) 30%
D) 20%
9.What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter
A) 2:1
B) 3:1
C) 4:1
D) 5:1
10.A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
A) 2 : 1
B) 3 : 2
C) 25 : 18
D) 27 : 20
Answers Key:
1. (B) Total volume of water displaced =(4 x 50)m^3 = 200 m^3
Rise in water level = 200/800 =0.25m = 25cm
2. (C) 1200
3. (D) Rs.876
surface area of a cube= 6*8*8 = 384sq.ft
quantity of paint required=(384/16)=24kg
cost of painting=36.5*24 = Rs.876
4. (A) 814
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm^2
Required number of tiles = 1517*902/41*41= 814
5. (A) 3:1
6. (B) 18cm
2(l+b)/b = 5/1
2l + 2b = 5b
3b = 2l
b =2/3 l
Then, Area = 216 cm^2
l x b = 216
l xl*2/3 l =216
l^2= 324
l = 18 cm.
7. (C) 6:1
Volume of the cube/volume of pyramid=a^3/1/3 a^3*a/2
8. (A) 50%
Let l, b the sides of the base, so that the area of the base = lb
remains constant.
Let ‘h’ be the height of the solid.
Volume of the solid, V = l× b× h.
Since the volume is to be increased by 50%
9. (B)
10. (C)
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