MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
ASSIGNMENT ON SURFACE AREAS AND VOLUMES Directions for 1 – 15: State true or false. 1.
A two–dimensional figure has no volume.
2.
A cuboid has six faces.
3.
The total surface area of a cuboid is lb + bh + lh
4.
100 cm2 = 1m2
5.
100 m3 = 10000 cm3
6.
The lateral surface area of a cuboid is 2h ( l + b )
7.
The faces of a cube are congruent to one another.
8.
Length of the diagonal of a cuboid is
9.
The length of the diagonal of a cube of side ‘a’ units is
10.
The curved surface area of a right circular cylinder is π dh.
11.
If the base radius and the height of a right circular cylinder are doubled, its total surface area will increase
l 2 + b2 + h 2 . 3 a units.
four times. 12.
The slant height of a right circular cone is always greater than its radius.
13.
A solid sphere has no plane surface.
14.
The total surface area of a solid sphere is twice that the surface area of a hemisphere of the same radius.
15.
If the radii and heights of a sphere and right circular cylinder are equal, then their volumes will be in the ratio 2 : 3.
16.
The length, breadth and height of a hall are 10 m, 8 m and 6 m, respectively. Find the cost of white– washing the walls and ceiling of the hall at the rate of Rs. 8 per m2
17.
The perimeter of the floor of a rectangular hall is 250 m. If the cost of painting the four walls at the rate of Rs. 8 per m2 is Rs. 12,000, find the height of the hall.
18.
Each edge of a cube is 8 cm. Find its lateral surface area and volume.
19.
A cubical box has its each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i)
Which box has the greater lateral surface area and by how much?
(ii)
Which box has greater volume and by how much?
20.
Three cubes of side 8 cm are joined together side–by–side. Find the surface area of the resulting cuboid.
21.
A sweet stall owner was placing an order for making card board boxes for packing sweets. Two sizes of boxes are required. The larger of dimensions 25 cm × 20 cm × 5 cm and the smaller of 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of cardboard is Rs. 4 per 100 cm2, find the cost of card board required for supplying 250 boxes of each size.
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MATHEMATICS ASSIGNMENT – IX STEPS … A TC Y P r og r am _________________________________________________________________________________
22.
The lateral surface area of a cubical box is 600 cm2. Find its total surface area.
23.
The lateral surface area of cube is 864 cm2. Find its total surface area and side.
24.
A cuboidal tin has dimensions 80 cm × 50 cm × 30 cm. Find the cost of making 40 such tin, if the cost of tin sheet is Rs. 95 per sq. meter.
25.
A big hall is 24 m long and 16 m wide. The total area of its four walls is equal to the sum of the areas of its floor and its flat roof. Find the height of the hall.
26.
A building is supported by 15 cylindrical pillars, all of the same size. Each pillar is 50 cm in diameter and 3.5 m in height. (i)
Find the curved surface area of each pillar.
(ii)
Find the cost of painting the curved surface of each pillar at the rate of Rs. 10 per m2.
27.
Curved surface area of a cylinder is 4620 cm2. Find its height if its diameter is 42 cm.
28.
Find the curved surface area of a closed cylindrical tank of radius 5.6 m and height 10 m. Also find the actual area of metal sheet required to make the tank, if 10% metal sheet is required extra.
29.
The height of a closed cylindrical tank is 20 m and radius of its base is 17.5 m. Find the ratio between its curved surface area and total surface area.
30.
A circus tent is in the shape of a cylinder up to a height of 8 m surmounted by a cone of the same radius 28 m. If the total height of the tent is 13 m, find its total inner curved surface area.
31.
The diameters of two cones are in the ratio 5 : 4 and their slant heights are in the ratio 3 : 8. Find the ratio between their curved surface areas.
32.
The circumference of the base of a 9 m high conical tent is 24π m. Find its curved surface area.
33.
The radius and slant height of a cone are in the ratio 5 : 13. If its curved surface area is 40040 cm2, find its height and total surface area.
34.
A right circular cylinder just encloses a sphere of radius ‘r’. (i)
Find the surface area of the sphere.
(ii)
Find the curved surface area of the cylinder.
(iii)
Find the ratio of the above two areas.
35.
The radii of two spheres are in the ratio 3 : 5. Find the ratio between their volumes.
36.
The diameter of the moon is approximately one fourth of that of the earth. Find the ratio between their surface areas.
37.
The total surface area of a solid hemisphere is 7392 cm2. Find its diameter.
38.
Find the diameter of the sphere whose surface area is 1386 cm2.
39.
Find the volume of a solid cube of side 12 cm. If it is cut into eight identical cubes, what will be the surface area of each small cube?
40.
A solid cube is cut into two cuboids of equal volume. Find the ratio between the surface area of the cube and that of each cuboid.
41.
The inner diameter of a spherical capsule is 3.5 mm. How much medicine is required to fill the capsule?
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MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
42.
The volumes of two spheres are in the ratio 1 : 8. Find the ratio between their (i) radii
43.
(ii) diameters
(iii) surface areas
A hollow spherical shell is made of iron sheet of thickness 1.5 cm. If its internal diameter is 12 cm, find the volume of iron in the sphere. Also find the mass of the shell if density of iron is 8.4 gm per cm3. (Take π = 3. 14)
44.
A cone of height 36 cm and a sphere have the same radii and same volumes. Find the radius of each solid.
45.
How many litres of milk can be filled in a hemispherical bowl of diameter 21 cm?
46.
A solid sphere of radius 5 cm is melted and recast into small identical spheres of radius 1 cm. How many such spheres can be made out of the big sphere?
47.
Three solid spheres of radii 1 cm, 6 cm and 8 cm are melted and recast into a single sphere. Find the radius of the sphere.
48.
The radius of a cone is halved and its height is doubled. Find the ratio between the heights of the resulting cone and the original cone.
49.
The height and slant height of a cone are 42 cm and 56 cm, respectively. Find its volume.
50.
A solid cone of diameter 20 cm and height 16 cm is melted and recast into another cone with half of its diameter. Find the height of the new cone.
51.
A right triangle ABC has sides AB = 8 cm, BC = 15 cm and AC = 17 cm. Find the volume of the soild formed when it is revolved about AB. (Take π = 3.14)
52.
A solid cylinder and a cone have the same base area. If the volume of the cylinder is twice the volume of the cone, find the ratio between their heights.
53.
The diameter of a wire is 6 mm and its length is 91 m. Find the weight of the wire if the density of the material used is 7.8 gm per cm3.
54.
The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 5 : 6. Find the ratio between their volumes and the ratio between their curved surface areas.
55.
Find the volume of the largest cylinder formed by rolling a rectangular sheet of dimensions 66 cm × 30 cm.
56.
A water reservoir is in the shape of a cuboid. Its length is 10 m. If 27 kilolitres of water is removed from the reservoir, the water level goes down by 45 cm. Find the width of the reservoir.
57.
A wooden block has dimensions 5m × 30 cm × 20 cm. How many planks of size 2.5 cm × 6 cm × 4 cm can be made out of it?
58.
A river is 3 m deep and 12 m wide and is flowing at the rate of 4.5 km per hour. How much water will fall into the sea in 5 minutes?
59.
If V is the volume of a cuboid, ‘S’ is the surface area and the dimensions are l × b × h , show that
1 2 ⎛1 1 1 ⎞ = ⎜ + + ⎟ V S ⎝l b h⎠
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MATHEMATICS ASSIGNMENT – IX STEPS … A TC Y P r og r am _________________________________________________________________________________
60.
The diameter and height of a cone are in the ratio 8 : 3 and its volume is 1356.48 cm3. Find its height and slant height. (Take π= 3.14)
ANSWER KEY SURFACE AREAS AND VOLUMES
1.
True
2.
True
3.
False
4.
False
5.
False
6.
True
7.
True
8.
True
9.
True
10.
True
11.
False
12.
True
13.
True
14.
False
15.
True
16.
Rs. 2368
17.
6m
18.
256 cm2, 512 cm3
19.
(i) The cubical box has more lateral surface area by 40 cm2 (ii) Volumes are equal
20.
896 cm2
21.
Rs. 21840
22.
900 cm2
23.
1296 cm2, 6 6 cm
24.
Rs. 6004
25.
9.6 m
26.
(i) 5.5 m2
27.
35 cm
28.
352 m2, 610.13 m2
29.
8 : 15
30.
3907.2 m2
31.
15: 32
32.
216 π m2
(ii) Rs. 55
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MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
33.
168 cm, 55440 cm2
34.
(i) 4 πr 2
35.
27 : 125
36.
1:16
37.
56 cm
38.
21 cm
39.
1728 cm3, 216 cm2
40.
3:2
41.
22.46 mm3
42.
(i) 1 : 2
(ii) 4 πr 2
(ii) 1 : 2
(iii) 1 : 1
(iii) 1 : 4
3
43.
861.26 cm , 7.240 kg
44.
9 cm
45.
2.425 litres
46.
125
47.
9 cm
48.
1:2
49.
60368 cm3
50.
64 cm
51.
1884 cm3
52.
2:3
53.
20.071 kg
54.
15:32, 5:8
55.
10395 cm3
56.
6m
57.
50
58.
13500 m3
60.
9 cm, 15 cm
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