Tricky questions of (Mensuration) for SSC CGL Tier-II 2016

Q1. The volume of cuboid is 6 times the volume of a cube. If the dimensions of the cuboid are 9 cm, 18 cm and 48 cm. The total surface area of the cube  
(a) 6912
(b) 13824
(c) 7776
(d) 25920
S1. Ans.(c)
Sol. Volume of cube = 6 × 9 × 18 × 48
= 2 × 3 × 3 × 3 × 2 × 3 × 3 × 4 × 4 × 3
Side of the cube = 4 × 3 × 3 = 36 cm
So, surface area of the cube =6×side^2 = 6 × 36 × 36
= 7776

Q2. If a cube maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to:  

Q3. A spherical steel ball was silver polished then it was cut into 4 similar pieces. What is the ratio of the polished area to the non-polished area:  
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) None of these

Q4. The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 sq. cm, its volume is: 
(a) 910 cm3
(b) 920 cm3
(c) 960 cn3
(d) 980 cm3

Q5. The base of a right prism is an equilateral triangle of area 173 cm^2 and the volume of the prism is 10380 cm3. The area of the lateral surface of the prism is use(√3=1.73) 
(a) 1200 cm^2
(b) 2400 cm^2
(c) 3600 cm^2
(d) 4380 cm^2

Q6. A hemisphere bowl B1 and a hollow right circular cylinder B2 (having length equal to its radius) have the same diameter equal to the length of a side of a hollow cubical box B3. Water is filled completely in all these vessels and the volumes of filled water are v1,v2 and v3 respectively in B1,B2 and B3 then:    
(a) V1<V2<V3
(b) V2<V3<V1
(c) V3<V2<V1
(d) V3<V1<V2

Q7. The height of a circular cylinder is increased by 6 times and base area is decreased by 1/9th times. By what factor its lateral surface area is increased? 
(a) 2
(b) 3
(c) 6
(d) 1.5

Q8. If from a circular sheet of paper of radius 15 cm, a sector of 144° is removed and the remaining is used to make a conical surface, then the angle at the vertex will be:

Q9. 250 men took a dip in a water tank at a time, which is 80m × 50m. What is the rise in the water level if the average displacement of 1 man is 4 m cubic?   
(a) 22 cm
(b) 25 cm
(c) 18 cm
(d) 30 cm

Q10. A solid is in the form of cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the total surface area of the solid. (Use = 22/7). 
(a) 398.75 cm2
(b) 418 cm2
(c) 444 cm2
(d) 412 cm2

Q11. Water flows out at the rate of 1000m/min from a cylindrical pipe of diameter 5 mm. Find the time taken to fill a conical tank whose diameter at the surface is 40 cm and depth 24 cm. 
(a) 50 min
(b) 102.4 min
(c) 51.2 min
(d) 25.6 min

Q12. Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
(a) 7 : 9
(b) 49 : 81
(c) 9 : 7
(d) 27 : 23

Q13. If the area of the circular shell having inner and outer radii of 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R_1 and height h, then h, in terms or R_1 will be

Q14. A rectangle water tank measure 15m × 6m at top and is 10 m deep. It is full of water. If water is drawn out lowering the level by 1 meter how much of water has been drawn out? 
(a) 90,000 litres
(b) 45,000 litres
(c) 80,000 litres
(d) 40,000 litres

Q15. The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in square metres) is:  
(a) 280
(b) 325
(c) 300
(d) 420


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