Advanced Quant Quiz For SSC Mains And SSC CHSL Exam

1. If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm^2 respectively, then the maximum length of a stick that can be placed in side the box is  

(a) 5 √2 cm   

(b) 5 cm  

(c) 6 cm   

(d) 2 √5 cm

2. A rectangular sheet of metal is 40 cm by 15cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open  rectangular box. The volume of the box is 

(a) 896 cm^3   

(b) 986 cm^3  

(c) 600 cm^3   

(d) 916 cm^3

3. A hall is 15m. long and 12m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, the volume of the hall, in cu. m, is 

(a) 720   

(b) 900  

(c) 1200 

(d) 1800 

4. 3 cubes each of edge 1 m, 6 m and 8 m respectively are melted into one single cube. The surface area of the new cube is: 

(a) 294 m^2   

(b) 324 m^2  

(c) 486 m^2   

(d) 468 m^2

5. The ratio of radii of two right circular cylinder is 2 : 3 and their heights are in the ratio 5: 4. The ratio of their curved surface area is 

(a) 5 : 6    

(b) 3 : 4   

(c) 4: 5   

(d) 2 : 3  

6. If cylinder A has three times the heights and one-third the diameter of cylinder B, then volume of A: volume of B equals

(a) 4 : 9    

(b) 9 : 1   

(c) 1: 3   

(d) 1 : 9

7. 10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4m. What is the cost of painting at the rate of Rs. 5 per square metre? 

(a) Rs. 400 

(b) Rs. 440  

(c) Rs. 480  

(d) Rs. 500 

8. A solid cylinder has total surface area of 462 cm^2. Its curved surface area is 1/3 rd of the total surface area. Then the radius of the cylinder is 

(a) 7 cm   

(b) 3.5 cm  

(c) 9 cm   

(d) 11 cm

9. The amount of cubic units of the volume of a sphere is double the amount of whole surface area of the same in square units, then the same radius of the  sphere is 

(a) 8 units  

(b) 5.5 units 

(c) 6 units  

(d) 10 units 

10. If the diameter of a sphere is doubled, how does its surface area change? 

(a) It increases two times.   

(b) It increases three times.

(c) It increases four times.  

(d) It increases eight times.

Answers and Solution:
1.(a)
If the three dimension of rectangular box are a,b,c.
then a+b+c = 12.......(1)
total surface area = 2(ab+bc+ca) = 94
By equation (1),(a+b+c)^2 = (12)^2
so a^2 + b^2 + c^2 + 2(ab+bc+ca) = 144
so a^2 + b^2 + c^2 + 94 = 144 => a^2 + b^2 + c^2 = 144-94 = 50
so maximum length = of stick = √(a^2 + b^2 + c^2) = √50 = 5√2 cm

2- (a)
After cutting 4 squares ,the remaining sheet
folded up to form an open rectangular box.'
so length of box = 40-(4+4) = 40-8 = 32 cm
Breadth of box = 15-(4+4) = 15 - 8 = 7 cm.
and depth of box = 4 cm.
so volume of the box = 32*7*4 = 896
3- (c)
A hall is 15 long and 12 m broad
let the hall is h meter high
so The area of (floor + Ceiling)= areas of 4 walls
so 2*15*12 = 2(15+12)h
so 2*15*12 = 2*27*h
=> h = 20/3 m
so The volume of hall = lbh = 15*12*20/3 =  1200 m^3
4- (c)

5- (a)
6- (c)
7- (b)
Curved surface area of a pillar = 2πrh
so curved surface area of 10 pillars = 2πrh*10 = 88
so cost of painting = 88*5 = Rs.440
8- (a)
9- (c)
let the radius of the sphere is x units
so volume of sphere = 2* whole surface area
so 4/3 πx^3 = 2 *4πx^2 => x = 6 units
10-(c)
let the diameter of sphere is 2r
so Surface area =  4πr^2
changed diameter = 2*2r = 4r
so changed radius = 2r
so changed surface area = 4π(2r)^2 = 4π.4r^2 = 16πr^2
                        = 4πr^2*4 = increase 4 times