Mathematics - Surface Areas and Volumes
Exam Duration: 45 Mins Total Questions : 30
The total surface area of a cylinder of height 6.5 cm is 220 sq cm. Find its volume.
- (a)
25.025 cm3
- (b)
2.5025 cm3
- (c)
2502.5 cm3
- (d)
250.25 cm3
A cylindrical vessel contains 49.896 litres of liquid. Cost of painting its C.S.A. at 2 paise/sq cm is Rs 95.04. What is its total surface area?
- (a)
5724 cm2
- (b)
7524 cm2
- (c)
5742 cm2
- (d)
7254 cm2
What is the ratio of volumes of two cones with the same radii?
- (a)
h1: h2
- (b)
r1:r2
- (c)
s1:s2
- (d)
1:2
The cost of painting the T.S.A. of cone at 5 ps/cm2 is Rs35.20. Determine the volume of the cone if its slant height is 25 cm.
- (a)
1223 cm2
- (b)
1232 cm2
- (c)
1323 cm2
- (d)
1332 cm2
A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. Find the volume of steel used.
- (a)
42.15 cm3
- (b)
41.52 cm3
- (c)
41.28 cm3
- (d)
45.21 cm3
How many litres of water flows out through a pipe having an area of cross section of 5 cm2 in one minute, if the speed of water in pipe is 30 cm/sec?
- (a)
9 litres
- (b)
15 litres
- (c)
30 litres
- (d)
3 litres
A well, 14 m deep is 2 m in radius. Find the cost of cementing the inner curved surface at the rate of Rs 2 per square metre.
- (a)
Rs 242
- (b)
Rs 352
- (c)
Rs 464
- (d)
Rs 294
The diameter of two cones are equal. If their slant heights are in the ratio 5: 4, find the ratio of their curved surface areas
- (a)
2:3
- (b)
4:5
- (c)
5:4
- (d)
3:2
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions? (Take \(\pi\)=\(\frac { 22 }{ 7 } \))
- (a)
11 sq.m
- (b)
16 sq.m
- (c)
28 sq.m
- (d)
44 sq.m
Into a conical tent of radius 7 m and vertical height 4.5 rn, how many full bags of rice can be emptied, if volume of each bag is 1.5 m3
- (a)
120 bags
- (b)
144 bags
- (c)
154 bags
- (d)
172 bags
Find the curved surface of a right circular cone, whose slant height and the base radius are 25 cm and 7 cm respectively.
- (a)
420 cm2
- (b)
550 cm2
- (c)
460 cm2
- (d)
580 cm2
A right circular cylinder has a height of 21 cm and base radius of 5 cm. Find the curved surface area of the cylinder.
- (a)
230 cm2
- (b)
660 cm2
- (c)
550 cm2
- (d)
450 cm2
If A1 A2 and A3 denote the areas of three adjacent faces of a cuboid, find its volume
- (a)
A1 A2 A3
- (b)
2A1 A2 A3
- (c)
\(\sqrt { { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 } } \)
- (d)
\(\sqrt [ 3 ]{ { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 } } \)
If each edge of a cube is increased by 50%, What is the percentage increase in its surface area?
- (a)
50 %
- (b)
75 %
- (c)
100 %
- (d)
125 %
Find the volume of a cube whose surface area is 150 cm2
- (a)
25 \(\sqrt { 5 } \)cm3
- (b)
64 cm3
- (c)
125 cm3
- (d)
27 cm3
If each edge of a cube of surface area S is doubled, what is the surface area of the new cube?
- (a)
2S
- (b)
4S
- (c)
6S
- (d)
8S
The circumference of the base of 9 m high wooden solid cone is 44 m.Find its volume.(Use \(\pi\)=\(\frac { 22 }{ 7 } \))
- (a)
235 m3
- (b)
456 m3
- (c)
365 m3
- (d)
462 m3
The largest sphere is carved out of a cube of side 7 cm. Find the volume of the sphere. (Take \(\pi \) = 3.14.)
- (a)
152.74 cm3
- (b)
243.41 cm3
- (c)
179.67 cm3
- (d)
195.01 cm3
The height of sand in a cylindrical box drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
- (a)
\(\frac { 24 }{ \sqrt { \pi } } \)
- (b)
\(\frac { 48 }{ \sqrt { \pi } } \)
- (c)
\(\frac { 32}{ \sqrt { \pi } } \)
- (d)
\(\frac { 48}{ \sqrt { \pi } } \)
If the diameter of the base of a closed right circular cylinder is equal to its height h, find its total surface area
- (a)
2\(\pi\)h2
- (b)
\(\frac { 3 }{ 2 } \)\(\pi\)h2
- (c)
\(\frac { 4 }{ 3 } \)\(\pi\)h2
- (d)
\(\pi\)h2
If the lateral surface area of a cube is 1600 cm2 what is its edge?
- (a)
15 cm
- (b)
18 cm
- (c)
20 cm
- (d)
25 cm
A cylinder and a cone have equal base radii and equal heights. If their curved surface areas are in the ratio 8: 5, what is the ratio of their radii to heights?
- (a)
8:5
- (b)
4:3
- (c)
3:4
- (d)
5:8
The radius of a cylinder is doubled and its height is halved. What is the change in its curved surface area?
- (a)
Halved
- (b)
Doubled
- (c)
Remains the same
- (d)
Becomes four times
A cube of edge 'k' is divided into 'n' equal cubes. Determine the edge of the new cube.
- (a)
\(\sqrt { n } k\)
- (b)
\(\frac { k }{ \sqrt [ 3 ]{ n } } \)
- (c)
\(\sqrt [ 3 ]{ nk } \)
- (d)
\(\frac { \sqrt [ 3 ]{ n } }{ k } \)
If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?
- (a)
4
- (b)
\(\frac{1}{\sqrt{2}}\)
- (c)
2
- (d)
\(1 \over 2\)
If the length of diagonal of a cube is \(\sqrt{12}\)cm, then the volume of the cube is
- (a)
8\(\sqrt{12}\) cm3
- (b)
8 cm3
- (c)
16\(\sqrt{2} cm^{3}\)
- (d)
16 cm3
A covered wooden box has the inner measures as 115 cm, 75 cm, 35 cm and the thickness of wood is 2.5 cm. Then the volume of the wood is ________.
- (a)
80000 cu. cm
- (b)
82125 cu. cm
- (c)
84000 cu. cm
- (d)
85000 cu. cm
Water flows in a tank 150 m\(\times\) 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep?
- (a)
50 hours
- (b)
150 hours
- (c)
100 hours
- (d)
200 hours
A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m\(\times\)25 m\(\times\)15 m. For how many days will the water of this tank last?
- (a)
30 days
- (b)
32 days
- (c)
40 days
- (d)
45 days
Read the statement carefully and write 'T' for true and 'F' for false.
(i) Volume of a cylinder is three times the volume of a cone on the same base and of same height.
(ii) Volume of biggest sphere in cube of edge 6 cm is 36ㅠ cm3.
(iii) Cuboids and cubes are special forms of right prisms.
- (a)
(i) (ii) (iii) T F T - (b)
(i) (ii) (iii) T T T - (c)
(i) (ii) (iii) F T F - (d)
(i) (ii) (iii) F T T