Q1.

If the heights of two right cicular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes ? 

  • 9 : 32

  • 8 : 30

  • 9 : 33

  • 5 : 35

Solution:

NA

Q2.

A sphere and a cube have equal surface areas . What is the ratio of the volume of the sphere to that of the cube ?  

  • \( \sqrt{6 \over \pi}\)

  • \(\)\({6 \over 2a}\)

  • 6\(\pi\)

  • 24

Solution:

NA

Q3.

Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes ? 

  • 3 : 1

  • 2 : 5

  • 1 : 5

  • 5 : 2

Solution:

NA

Q4.

The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular end is 4 cm, write the height of the frustum. 

  • 2 cm

  • 5 cm

  • 3 cm

  • 6 cm

Solution:

NA

Q5.

The radius of the sphere is increased by 5%. Find the % increase in its surface area .

  • 10

  • 11

  • 12

  • 10.25

Solution:

NA

Q6.

If the radius of a cylinder is doubled and the height is halved , what is the ratio between the new volume and the previous volume ? 

  • 2 : 1

  • 1 : 2

  • 2 : 5

  • 3 : 4

Solution:

NA

Q7.

A cylindrical container of diameter 8 cm contains water . A solid sphere of diameter 6 cm is lowered into the water until it is completely immersed . Because of this the vessel will rise by __________ cm .  

  • 6 

  • 2.25

  • 2

  • 3

Solution:

NA

Q8.

The diameter of cross - section of a wire is reduced by 5% , how much percent will the length be increased so that the volume remains same as (No change in volume) . 

  • 10.8%

  • 11.5%

  • 12 %

  • 10 %

Solution:

NA

Q9.

Water is flowing at the rate of 3 km/hr through a circular pipe of 10 cm internal radius into a circular cistern of diameter radius 5 meter and length one meter . In how much time will the cistern be filled . 

  • 60 min

  • 50 min

  • 55 min

  • 40 min

Solution:

NA

Q10.

Find the maximum volume of a cone that can be carved out of solid hemisphere of diameter 2 cm . 

  • \( {\pi \over 3}\)

  • \( {\pi \over 8}\)

  • 7

  • 10

Solution:

NA

Q11.

The radius of a sphere is increased by 10%.Then  volume will be increased by ______ % .

  • 23.2%

  • 33.1%

  • 45.2%

  • 32%

Solution:

NA

Q12.

The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be\({1 \over 64}\) of the volume of the given cone ,find the height of small cone . 

  • 10

  • 11

  • 15

  • 9

Solution:

NA

Q13.

A right triangle, whose sides are 15cm, 20 cm anfd 25 cm is made to revolve about its hypotenuse. Find the volume of the double cone so formed .  

  • 3768 cm3

  • 3654 cm3

  • 4000 cm3

  • 3214 cm3

Solution:

NA

Q14.

If a cone, a hemisphere and a cylinder have equal bases and have same height , then the raio of their volumes is 

  • 1 : 3 : 2

  • 2 : 3 : 1 

  • 2 : 1 : 3

  • 1 : 2 : 3 

Solution:

NA

Q15.

A cylindrical cistern whose base is horizontal and diameter is 7 cm contains sufficient water so that when a sphere is placed in a cistern , the water just covers the sphere (the sphere just fits into the cistern). Find the depth of water in the cistern before the sphere was put into the cistern . 

  • 7/3 cm

  • 1/2 cm 

  • 3/4 cm 

  • 9/7 cm 

Solution:

NA