EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 14.00 cm and base radius 7.00 cm, a conical cavity of height 10.00 cm and base radius 7.00 cm is drilled out. Find the volume of the resulting solid

(i)

1862.67 cu.cm
(ii)

1622.67 cu.cm
(iii)

1482.67 cu.cm
(iv)

1642.67 cu.cm
(v)

1812.67 cu.cm

Question 2

2.

A solid metallic cylinder of base radius 15.00 cm and height 25.00 cm is melted to form cones each of height 1.00 cm and radius 1.00 cm . Find the number of complete cones formed

(i)

16175
(ii)

18475
(iii)

19275
(iv)

15075
(v)

16875

Question 3

3.

A conical vessel, whose internal radius is 4.50 cm and height 9.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 1.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

60.75 cm
(ii)

55.75 cm
(iii)

57.75 cm
(iv)

63.75 cm
(v)

65.75 cm

Question 4

4.

From a circular cylinder of diameter 15.00 cm and height 19.00 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid.

(i)

2239.29 cu.cm
(ii)

2499.29 cu.cm
(iii)

2119.29 cu.cm
(iv)

2379.29 cu.cm

Question 5

5.

A cone of maximum volume is carved out of a cube of edge 10.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

723.10 cu.cm
(ii)

764.10 cu.cm
(iii)

720.10 cu.cm
(iv)

744.10 cu.cm
(v)

738.10 cu.cm

Question 6

6.

A cone of maximum volume is carved out of a cuboid of dimensions 13.00 cm✕13.00 cm✕30.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

3882.14 cu.cm
(ii)

3592.14 cu.cm
(iii)

3742.14 cu.cm
(iv)

3602.14 cu.cm
(v)

4012.14 cu.cm

Question 7

7.

An open cylindrical vessel of internal diameter 28.00 cm and height 26.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 14.00 cm and height 26.00 cm and filled with water. If the cone is replaced by another cone whose height is 7.80 cm and base radius is 4.20 cm, find the drop in the water level.

(i)

9.93 cm
(ii)

1.93 cm
(iii)

3.93 cm
(iv)

0.93 cm
(v)

2.93 cm

Question 8

8.

A cylindrical vessel of base radius 24.00 cm contains water . A solid sphere of radius 20.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

15.52 cm
(ii)

21.52 cm
(iii)

18.52 cm
(iv)

13.52 cm
(v)

23.52 cm

Question 9

9.

Marbles of diameter 1.80 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 7.2 cm. If the diameter of the beaker is 18.00 cm, find the number of marbles that are dropped in it

(i)

588
(ii)

612
(iii)

600
(iv)

624
(v)

587

Question 10

10.

A solid consisting of a right circular cone, standing on a hemisphere is placed upright, in a right circular cylinder full of water and touches the bottom. The radius of the cylinder is 12.50 cm and height is 27.50 cm. The radius of the hemisphere is 7.50 cm and the height of the cone is 18.00 cm. Find the volume of water left in the cylinder.

(i)

12059.82 cu.cm
(ii)

11559.82 cu.cm
(iii)

13259.82 cu.cm
(iv)

10759.82 cu.cm
(v)

10359.82 cu.cm

Question 11

11.

A solid consists of a right circular cylinder with a hemisphere on one end and a cone on the other . The radius and height of the cylindrical part are 8.50 cm and 24.50 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the volume of the solid, if the height of the conical part is 14.00 cm

(i)

8049.65 cu.cm
(ii)

7909.65 cu.cm
(iii)

7749.65 cu.cm
(iv)

7829.65 cu.cm
(v)

7939.65 cu.cm

Question 12

12.

A conical vessel of radius 6.00 cm and height 8.00 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. Find the fraction of the water that overflows

(i)

1
8
(ii)

1
2
(iii)

5
8
(iv)

3
10
(v)

3
8

Question 13

13.

A well of diameter 10.00 m is dug to a depth of 17.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 27.00 m✕19.00 m . Find the height of the platform

(i)

1.60 m
(ii)

2.60 m
(iii)

4.60 m
(iv)

0.60 m
(v)

3.60 m

Question 14

14.

A well of diameter 13.00 m is dug to a depth of 15.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 11m to form an embankment. Find the height of the embankment.

(i)

4.40 m
(ii)

3.40 m
(iii)

1.40 m
(iv)

0.40 m
(v)

2.40 m

Question 15

15.

An ice cream container has the shape of a right circular cylinder having inner diameter 34.00 cm and height 43.00 cm . The ice cream is filled into cones of diameter 20.00 cm and height 14.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

13
(ii)

7
(iii)

5
(iv)

10
(v)

15

Question 16

16.

Water in a canal, 11 m wide and 2 m deep is flowing with a speed of 12 kmph . How much area will it irrigate in 35 min, if 7 cm of standing water is needed ?

(i)

2150000.00 sq.m
(ii)

2200000.00 sq.m
(iii)

2330000.00 sq.m
(iv)

2320000.00 sq.m
(v)

1940000.00 sq.m

Question 17

17.

A farmer connects a pipe of internal diameter
10 cm

from a canal into a cylindrical tank in his field,

which is
10 m
in diameter and
1 m
deep.

If water flows through the pipe at the rate of
25
2

kmph
,

in how much time will the tank be filled ?

(i)

51.00 min
(ii)

48.00 min
(iii)

43.00 min
(iv)

45.00 min
(v)

53.00 min

Assignment Key