EduSahara™ Assignment
Name : Conversion of Solid from One Shape to Another
Chapter : Mensuration
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The height of a right circular cone is 5.00 cm and the radius of its base is 8.50 cm. It is melted and recast into a right circular cone with base radius 4.25 cm. Find the new height
(i)
25.00 cm
(ii)
17.00 cm
(iii)
23.00 cm
(iv)
15.00 cm
(v)
20.00 cm
Question
2
2.
A solid metallic cylinder of base radius 11.50 cm and height 14.00 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)
5394
(ii)
5674
(iii)
5434
(iv)
5554
(v)
5704
Question
3
3.
A conical vessel, whose internal radius is 8.50 cm and height 29.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 5.00 cm. Find the height to which the liquid rises in the cylindrical vessel.
(i)
22.94 cm
(ii)
32.94 cm
(iii)
30.94 cm
(iv)
27.94 cm
(v)
24.94 cm
Question
4
4.
A hollow metallic cylindrical tube has an internal radius of 14.50 cm and height 22.00 cm. The thickness of the metal is 2 cm .The tube is melted to cast into a right circular cone of height 6.00 cm. Find the radius of the cone.
(i)
31.12 cm
(ii)
29.12 cm
(iii)
23.12 cm
(iv)
21.12 cm
(v)
26.12 cm
Question
5
5.
An open cylindrical vessel of internal diameter 30.00 cm and height 17.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 15.00 cm and height 17.00 cm and filled with water. If the cone is replaced by another cone whose height is 10.20 cm and base radius is 3.75 cm, find the drop in the water level.
(i)
1.20 cm
(ii)
2.20 cm
(iii)
9.20 cm
(iv)
0.20 cm
(v)
3.20 cm
Question
6
6.
The surface area of a solid metallic sphere is 5028.57 sq.cm. It is melted and recasted into solid right circular cones of radius 10.00 cm and height 12.00 cm . Find the number of complete cones that can be made
(i)
31
(ii)
23
(iii)
29
(iv)
21
(v)
26
Question
7
7.
A hollow sphere of internal and external diameters 32.00 cm and 40.00 cm respectively is melted into a cone of base diameter 10.00 cm. Find the height of the cone
(i)
640.64 cm
(ii)
606.64 cm
(iii)
648.64 cm
(iv)
624.64 cm
(v)
621.64 cm
Question
8
8.
A cylindrical vessel of base radius 22.00 cm contains water . A solid sphere of radius 19.00 cm is immersed completely in the water. Find the rise in the water level in the vessel
(i)
13.90 cm
(ii)
18.90 cm
(iii)
21.90 cm
(iv)
15.90 cm
(v)
23.90 cm
Question
9
9.
Marbles of diameter 1.40 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 11.2 cm. If the diameter of the beaker is 19.60 cm, find the number of marbles that are dropped in it
(i)
2282
(ii)
2082
(iii)
2592
(iv)
2352
(v)
2432
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 9.00 cm and height is 20.00 cm. The radius of the hemisphere is 7.00 cm and the height of the cone is 13.00 cm. Find the volume of water left in the cylinder.
(i)
3875.43 cu.cm
(ii)
3885.43 cu.cm
(iii)
3565.43 cu.cm
(iv)
3475.43 cu.cm
(v)
3705.43 cu.cm
Question
11
11.
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)
3
8
(ii)
3
10
(iii)
1
8
(iv)
1
2
(v)
5
8
Question
12
12.
A metallic sphere of radius 10.00 cm is melted to recast into the shape of a cylinder of radius 13.00 cm . Find the height of the cylinder.
(i)
9.89 cm
(ii)
8.89 cm
(iii)
5.89 cm
(iv)
6.89 cm
(v)
7.89 cm
Question
13
13.
Metallic spheres of radii 7.00 cm, 4.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.
(i)
407
cm
(ii)
5
√
407
cm
(iii)
3
√
409
cm
(iv)
3
√
404
cm
(v)
3
√
407
cm
Question
14
14.
A well of diameter 15.00 m is dug to a depth of 14.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 17.00 m✕21.00 m . Find the height of the platform
(i)
7.93 m
(ii)
5.93 m
(iii)
4.93 m
(iv)
6.93 m
(v)
8.93 m
Question
15
15.
A well of diameter 10.00 m is dug to a depth of 20.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 13m to form an embankment. Find the height of the embankment.
(i)
2.67 m
(ii)
0.67 m
(iii)
9.67 m
(iv)
1.67 m
(v)
3.67 m
Question
16
16.
An ice cream container has the shape of a right circular cylinder having inner diameter 24.00 cm and height 32.00 cm . The ice cream is filled into cones of diameter 18.00 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)
6
(ii)
5
(iii)
7
(iv)
3
(v)
4
Question
17
17.
A cylinder with radius 7.00 cm and height 2.00 cm is melted to recast into a cone of height 294.00 cm. Find the radius of the cone.
(i)
3.00 cm
(ii)
0.00 cm
(iii)
9.00 cm
(iv)
1.00 cm
(v)
2.00 cm
Question
18
18.
A copper sphere having a radius of 10.00 cm is melted and drawn into a cylindrical wire of radius 0.60 cm. Calculate the length of the wire.
(i)
42.04 m
(ii)
40.04 m
(iii)
34.04 m
(iv)
37.04 m
(v)
32.04 m
Question
19
19.
A copper rod of diameter 1.40 cm and length 16.00 cm is drawn into a wire of length 31.36 m of uniform thickness. Find the thickness of the wire.
(i)
1
20
cm
(ii)
3
20
cm
(iii)
0
cm
(iv)
1
5
cm
(v)
1
10
cm
Assignment Key
1) (v)
2) (iv)
3) (iv)
4) (v)
5) (i)
6) (v)
7) (iv)
8) (ii)
9) (iv)
10) (v)
11) (i)
12) (v)
13) (v)
14) (iv)
15) (iv)
16) (ii)
17) (iv)
18) (iv)
19) (i)
