Sphere Questions for CAT PDF

0
529
Sphere Questions for CAT PDF
Sphere Questions for CAT PDF

Sphere Questions for CAT PDF

Download important CAT Sphere Questions with Solutions PDF based on previously asked questions in CAT exam. Practice Sphere Questions with Solutions for CAT exam.

Download Sphere Questions for CAT PDF

3 Months Crash Course for CAT

Download CAT Quant Questions PDF

Take a free mock test for CAT

Question 1: It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.

a) 2.2 liters

b) 2.5 liters

c) 3.0 liters

d) 4.0 liters

e) None of the above

Question 2: If a right circular cylinder of height 14 cm is inscribed in a sphere of radius 8  cm, then the volume of the cylinder is:

a) 110 cm3

b) 220 cm3

c) 440 cm3

d) 660 cm3

Question 3: A cylinder, a Hemi-sphere and a cone stand on the same base and have the same heights. The ratio of the areas of their curved surface is:

a) 2:2:1

b) 2:2:1

c) 2:3:1

d) None of the above

Question 4: Consider the volumes of the following objects and arrange them in decreasing order:
i. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
ii. A cube of each side 4 cm.
iii. A cylinder of radius 3 cm and length 3 cm
iv. A sphere of radius 3 cm

a) iv,iii,ii,i

b) iv,ii,iii,i

c) iv,iii,i,ii

d) None of the above

Question 5: A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

a) 1000 times

b) 100 times

c) 10 times

d) No change

e) None of the above

Take a free CAT online mock test

Take a free mock test for CAT

Download CAT Syllabus PDF

Answers & Solutions:

1) Answer (D)

2 litres are required to paint the surface of a solid sphere.
Surface area of the solid sphere = 4πr2
Now, the solid sphere is cut into 4 identical parts. This is possible only when the sphere is cut into 4 quarter spheres.
After making the first cut, 2 hemispheres will be formed. 2 circles of area πr2 will get exposed in addition to the surface area of the sphere (the base surface of the bottom hemisphere and the base of the top hemisphere).
Now, another perpendicular cut will be made along the diameter of the sphere. 2 additional surfaces will get exposed again (one on left hemisphere and the another on the right hemisphere).

Area exposed after making 4 identical pieces = 4πr22πr22πr2
8πr2
2 litres of paint is required to paint an area of 4πr2
=> 4 litres of paint will be required to paint an area of 8πr2.

Therefore, option D is the right answer.

2) Answer (D)

8

The radius of sphere is 8 cm. Then applying Pythagoras, the radius of base of cylinder is 15  cm

The height of cylinder is given as 14 cm. Volume of cylinder is π r2h

227* 15*14 = 660 cm3

3) Answer (D)

The cylinder, hemisphere and cone stand on the same base and have the same height. Let the radius of the three solids be r and the height be h.

Height of the hemisphere, h = r (Radius)

Curved surface area of the cylinder = 2πrr = 2πr2
Curved surface area of the hemisphere = 2πr2
Curved surface area of the cone = πrr2+r2 = πrr2+r2 = πr22
Ratio = 2:2:2 = 2:2:1
As the answer is not among the given options, option D is the right answer.

4) Answer (A)

i. Volume of the parallelepiped of length 5 cm, breadth 3 cm and height 4 cm = 3*4*5 = 60 cm3
ii. Volume  of the cube of each side 4 cm = 4^3 = 64 cm3
iii.Volume  of the cylinder of radius 3 cm and length 3 cm = π323 = 84.82 cm3
iv. Volume  of the  sphere of radius 3 cm = 4/3π33 = 113.09 cm3

Therefore, we can say that volumes of the objects in decreasing order = iv,iii,ii,i.

Hence, option A is the correct answer.

5) Answer (E)

Radius of larger sphere = R=10 cm

Let radius of each of the smaller spheres = r cm

=> 43πR3=1000×43πr3

=> 103=1000r3

=> r=13=1 cm

Initial surface area of sphere = 4πR2=4π×100=400π

Final surface area of 1000 spheres = 1000×4πr2=1000×4π=4000π

Increase in surface area = 4000π400π=3600π

=> 3600π400π=9 times

Download CAT Previous Papers PDF

Download Free CAT Preparation App

We hope this CAT Sphere Questions with Solutions PDF for CAT will be helpful to you.

LEAVE A REPLY

Please enter your comment!
Please enter your name here