EduSahara™ Assignment
Name : Similarity as a Size Transformation
Chapter : Similarity
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
△ABC is a triangle with sides BC = 12 cm, CA = 11 cm and AB = 14 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 9.78 cm. Find the scale factor.
(i)
8
7
(ii)
8
9
(iii)
2
3
(iv)
8
11
(v)
10
9
Question
2
2.
△ABC is a triangle with sides BC = 11 cm, CA = 14 cm and AB = 12 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 7.86 cm. Find the corresponding lengths of the reduced triangle △A'B'C'.
(i)
6.86 cm, 9 cm, 7.57 cm
(ii)
5.86 cm, 8 cm, 6.57 cm
(iii)
8.86 cm, 11 cm, 9.57 cm
(iv)
9.86 cm, 12 cm, 10.57 cm
(v)
7.86 cm, 10 cm, 8.57 cm
Question
3
3.
AB = 18.00 cm, BC = 7.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 13000. Calculate the diagonal distance of the field.
(i)
4.51 km
(ii)
3.51 km
(iii)
0.51 km
(iv)
2.51 km
(v)
1.51 km
Question
4
4.
AB = 19.00 cm, BC = 18.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 5000. Calculate the area of the field.
(i)
2.85 sq.km
(ii)
7.86 sq.km
(iii)
1.85 sq.km
(iv)
0.85 sq.km
(v)
8.86 sq.km
Question
5
5.
The measurements of a triangular field △ABC are BC = 11 cm, AB = 8 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 19000. Calculate the actual length of CA in km.
(i)
4.58 km
(ii)
0.58 km
(iii)
2.58 km
(iv)
1.58 km
(v)
3.58 km
Question
6
6.
The measurements of a triangular field △ABC are BC = 9 cm, AB = 10 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 18000. Calculate the actual area of the plot in sq.km.
(i)
2.46 sq.km
(ii)
3.46 sq.km
(iii)
1.46 sq.km
(iv)
9.46 sq.km
(v)
0.46 sq.km
Question
7
7.
A triangle having an area 133.93 sq.cm is enlarged by a scale factor of 2.50. Find the area of its image.
(i)
837.06 sq.cm
(ii)
819.06 sq.cm
(iii)
851.06 sq.cm
(iv)
815.06 sq.cm
(v)
864.06 sq.cm
Question
8
8.
A triangle having an area 23.66 sq.cm is reduced such that the area of its image is 18.33 sq.cm. Find the scale factor.
(i)
1.88
(ii)
0.88
(iii)
2.88
(iv)
8.88
(v)
7.88
Question
9
9.
A rectangle having an area 180.00 sq.cm is enlarged by a scale factor of 1.33. Find the area of its image.
(i)
331.40 sq.cm
(ii)
302.40 sq.cm
(iii)
318.40 sq.cm
(iv)
293.40 sq.cm
(v)
332.40 sq.cm
Question
10
10.
A rectangle having an area 135.00 sq.cm is reduced such that the area of its image is 14.70 sq.cm. Find the scale factor.
(i)
0.33
(ii)
1.33
(iii)
8.33
(iv)
7.33
(v)
2.33
Question
11
11.
A model of a ship is made to a scale of 1 : 150. If length of the model ship is 20 m, calculate the length of the ship.
(i)
2880.00 m
(ii)
3040.00 m
(iii)
2940.00 m
(iv)
3150.00 m
(v)
3000.00 m
Question
12
12.
A model of a ship is made to a scale of 1 : 115. If the length of the ship is 1035 m, calculate length of the model ship.
(i)
9.00 m
(ii)
7.00 m
(iii)
11.00 m
(iv)
8.00 m
(v)
10.00 m
Question
13
13.
A model of a ship is made to a scale of 1 : 65. If the area of the deck of the model ship is 36 sq.m, calculate the area of the deck of the ship.
(i)
128100.00 sq.m
(ii)
180100.00 sq.m
(iii)
152100.00 sq.m
(iv)
136100.00 sq.m
(v)
164100.00 sq.m
Question
14
14.
A model of a ship is made to a scale of 1 : 70. If the area of the deck of the ship is 19600 sq.m, calculate the area of the deck of the model ship.
(i)
6.00 sq.m
(ii)
3.00 sq.m
(iii)
4.00 sq.m
(iv)
2.00 sq.m
(v)
5.00 sq.m
Question
15
15.
A model of a ship is made to a scale of 1 : 180. If the volume of the model ship is 8 cu.m, calculate the volume of the ship.
(i)
46656000.00 cu.m
(ii)
47156000.00 cu.m
(iii)
45256000.00 cu.m
(iv)
44356000.00 cu.m
(v)
49456000.00 cu.m
Question
16
16.
A model of a ship is made to a scale of 1 : 180. If the volume of the ship is 23887872000 cu.m, calculate the volume of the model ship.
(i)
4096.00 cu.m
(ii)
4256.00 cu.m
(iii)
4266.00 cu.m
(iv)
3916.00 cu.m
(v)
3946.00 cu.m
Question
17
17.
The dimensions of the model of a multi-storey building are 8 cm ✕ 8 cm ✕ 4 cm. If the model is drawn to a scale of 1 : 150, find the actual dimensions of the building.
(i)
1200 cm ✕ 1200 cm ✕ 601 cm
(ii)
1200 cm ✕ 1201 cm ✕ 600 cm
(iii)
1200 cm ✕ 1200 cm ✕ 600 cm
(iv)
1201 cm ✕ 1200 cm ✕ 600 cm
(v)
1201 cm ✕ 1201 cm ✕ 600 cm
Question
18
18.
The dimensions of the model of a multi-storey building are 1 cm ✕ 6.5 cm ✕ 9.5 cm. If the model is drawn to a scale of 1 : 145, find the floor area of a room of the building whose area in the model is 49 sq.cm.
(i)
75.02 sq.m
(ii)
88.02 sq.m
(iii)
103.02 sq.m
(iv)
116.02 sq.m
(v)
129.02 sq.m
Question
19
19.
The dimensions of the model of a multi-storey building are 9.5 cm ✕ 4 cm ✕ 9.5 cm. If the model is drawn to a scale of 1 : 140, find the volume of the room in the model whose actual volume is 11239.424 cu.m.
(i)
4076.00 cu.cm
(ii)
4096.00 cu.cm
(iii)
4326.00 cu.cm
(iv)
4176.00 cu.cm
(v)
3846.00 cu.cm
Question
20
20.
A model of building is made with a scale factor of 1 : 70. Find the actual height of the building if the height of the model is 3 cm.
(i)
2.10 m
(ii)
0.10 m
(iii)
4.10 m
(iv)
1.10 m
(v)
3.10 m
Question
21
21.
A model of building is made with a scale factor of 1 : 60. Find the volume of the tank on the top of the model if its actual volume is 729000 cu.cm.
(i)
4.38 cu.cm
(ii)
1.38 cu.cm
(iii)
5.38 cu.cm
(iv)
2.38 cu.cm
(v)
3.38 cu.cm
Assignment Key
1) (ii)
2) (v)
3) (iv)
4) (iv)
5) (iii)
6) (iii)
7) (i)
8) (ii)
9) (iii)
10) (i)
11) (v)
12) (i)
13) (iii)
14) (iii)
15) (i)
16) (i)
17) (iii)
18) (iii)
19) (ii)
20) (i)
21) (v)
