Advanced Quant Quiz For SSC Mains And SSC CHSL Exam

1. A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, the n the ratio of radius and height of its conical part is 

(a) 1 : 3   

(b) 1 : 1  

(c) √3 : 1  

(d) 1 : √3

2.The radii of a sphere and a cone are equal. If their volumes are equal, the ratio of the height and the radius of the base of the cone is 

(a) 1 : 2   

(b) 1 : 4  

(c) 4 : 1  

(d) 2 :  1 

3. The volumes of a sphere and a right circular cone are same. The height of the cone is half of the radius of its base. The ratio of areas of  the curved surface of the cone and the sphere is 

(a) 2 : √5  

(b) √5 : ∛16  

(c) √5 : 2  

(d) 4 : √5

4.A child reshapes a cone made up of clay of height 24 cm and radius 6 cm into a sphere. The radius (in cm) of the sphere is 

(a) 6  

(b) 12  

(c) 24  

(d) 48

5. A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, the ratio of their radius and height is 

(a) 1 : 2   

(b) 1 : 3  

(c) 2 : 3  

(d) 3 : 4

6. A sphere is inscribed in a cubical box such that the sphere is tangent to all six facts of the box. What is the ratio of the volume of the cubical box to volume of sphere? 

(a) 6π    

(b) 36π  

(c) 4 π/3  

(d) 6/ π

7. The ratio of the volume of a cube and of a solid sphere is 363 : 49. The ratio of an edge of the cube and the radius of the sphere is (take π=22/7) 

(a) 7 : 11   

(b) 22 : 7  

(c) 11 : 7  

(d) 7 : 22

8. A cone, a hemisphere and a cylinder stand on equal base and have the same height. Their volumes are in the ratio 

(a) 1 : 3 : 2   

(b) 2 : 3 : 1  

(c) 1: 2 : 3  

(d) 3 : 1 : 2 

9. The radii of the circular ends of a bucket of height 40 cm are of lengths 35 cm and 14 cm. What is the volume of the bucket? 

(a) 60060 cubic cm 

(b) 70040 cubic cm

(c) 80080 cubic cm

(d) 80160 cubic cm

10. An edge of cube is increased by 50%. Then percent increase in total surface area is: 

(a) 100%  

(b) 75%   

(c) 250%  

(d) 125%

Answers Key:
1- (d)
2- (c)
3- (c)
4- (a)
5- (d)
6- (d)
7- (b)
8- (c)
9- (c)
10- (d)