NTSE SAT Mathematics - Volume and Surface Area
Exam Duration: 45 Mins Total Questions : 25
A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is
- (a)
66\(\frac{2}{3}\)%
- (b)
78\(\frac{1}{2}\)%
- (c)
100%
- (d)
none of these
A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be
- (a)
1:2
- (b)
2:1
- (c)
1:\(\sqrt2\)
- (d)
\(\sqrt2\):1
A cone of height 9 cm with diameter of its base is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is
- (a)
25%
- (b)
25.5%
- (c)
50%
- (d)
75%
The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 em and base radius 3 cm is
- (a)
460
- (b)
500
- (c)
600
- (d)
640
The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 krn2, The height of the mountain is
- (a)
2.2 km
- (b)
2.4 km
- (c)
3 km
- (d)
3.11 km
A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as.12 cm. The height of the cone is
- (a)
2 cm
- (b)
3 cm
- (c)
4 cm
- (d)
6 cm
The diameter of the iron ball used for the shot-put game is 14 cm. It is melted and then a solid cylinder of height 2 1/3 cm is made. What will be the diameter of the base of the cylinder?
- (a)
14 cm
- (b)
14/3 cm
- (c)
28 cm
- (d)
28/3 cm
A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then
- (a)
H=2R
- (b)
H=3R
- (c)
H=\(\sqrt{3}\) R
- (d)
H=\(\frac{2}{3}\)R
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is
- (a)
12 cm
- (b)
14 cm
- (c)
15 cm
- (d)
18 cm
In what ratio are the volu.mes of a cylinder, a cone and a sphere, if each has the same diameter and the same height?
- (a)
1:3:2
- (b)
2:3:1
- (c)
3:1:2
- (d)
3:2:1
The slant height of the frustrum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustrum?
- (a)
38 cm2
- (b)
25 cm2
- (c)
48 cm2
- (d)
none of these
A cistern 6m long and 4m wide contains water up to a depth of 1m 25cm. The total area of the wet surface
- (a)
49m2
- (b)
50m2
- (c)
53.5m2
- (d)
55m2
The capacity of a tank of dimensions (8m x 6m x 2.5m) is
- (a)
120 litres
- (b)
1250 litres
- (c)
12000 litres
- (d)
120000 litres
If a metallic cuboids weighs 16 kg, how much would a miniature cuboid of metal weigh, if all dimension are reduced to one fourth of the origin
- (a)
0.25 kg
- (b)
0.50 kg
- (c)
0.75 kg
- (d)
1 kg
A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is
- (a)
\(\sqrt { \pi } :\sqrt { 6 } \)
- (b)
\(\sqrt { 2 } :\sqrt { \pi } \)
- (c)
\(\sqrt { \pi } :\sqrt { 3 } \)
- (d)
\(\sqrt { 6 } :\sqrt { \pi } \)
The capacities of two hemispherical vessels are 6.41itres and 21.6 litters. The areas of inner curved surfaces of the vessels will be in the ratio of
- (a)
\(\sqrt { 2 } :\sqrt { 3 } \)
- (b)
2:3
- (c)
4:9
- (d)
16:81
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the new sphere will be
- (a)
12 cm
- (b)
24 cm
- (c)
30 cm
- (d)
36 cm
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 em, The height of the cone is
- (a)
12 cm
- (b)
14 cm
- (c)
15 cm
- (d)
18 cm
How many cubes of 3 em edge can be cut out of a cube of 18 cm edge?
- (a)
36
- (b)
216
- (c)
218
- (d)
432
A cuboidal black of 6 cm \(\times\) 9 cm \(\times\) 12 em is cut up into an exact number of equal cubes. The least possible number of cubes will be
- (a)
6
- (b)
9
- (c)
24
- (d)
30
If each edge of a cube is doubled, then the volume:
- (a)
is doubled
- (b)
becomes 4 times
- (c)
becomes 6 times
- (d)
becomes 8 times
Three cubes with sides in the ratio 3:4: 5 are melted to form a single cube whose diagonal is 12\(\sqrt3\) cm. The sides of the cubes are
- (a)
3 cm, 4 cm, 5 cm
- (b)
6cm, 8 cm, 10 cm
- (c)
9 cm, 12 cm, 15 cm
- (d)
none of these
If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2, The radius of the sphere before the increase was?
- (a)
3 cm
- (b)
4 cm
- (c)
5 cm
- (d)
6 cm
What is the capacity of the cylindrical tank?
I. Radius of the base is half of its height which is 28m
II. Area of the base is 616 square metres and its height is 28 m
- (a)
data either in statement I or II alone are sufficient to answer
- (b)
date in both statements I and II together are necessary to answer
- (c)
data in statement II alone are sufficient to answer
- (d)
none of these
A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut sphere is
- (a)
3:2
- (b)
4:1
- (c)
4:3
- (d)
7:4
