Real Life Applications of Similarity

Q. A model of a boat is made on the scale of $1:5$. The full size of the boat has a length of $300cm$ and width of $80cm.$ What is the width of the scale model?

1. $400$ cm
2. $16$ cm
3. $80$ cm
4. None of the above

Q. If any two dimensional figure is enlarged by a scale factor of 2, the area of the enlarged figure is times the area of the original figure.

Q.

A car manufacturer also produces exact scale models of the cars. The fuel tank of the real car has a volume of 64 liters, and that of the model car has a volume of 0.512 liters. If the length of the real car is 5 meters , what is the length of the model car?

Q. On a map with a scale factor $1:10,000,$ the distance between two nearby cities is $4\text{inches}.$ Find the actual distance between the two cities in miles (correct upto $2$ decimal places).

1. $1.26$
2. $0.63$
3. $63.00$
4. None of the above.

Q. A rectangle has the dimensions of $8ft\times 4ft.$ Calculate the area of the rectangle produced when it is scaled by a scale factor of 4.

1. $128f{t}^2$
2. $512f{t}^2$
3. $256f{t}^2$
4. $1024f{t}^2$

Q. A similar fencing has to be built around a rectangular swimming pool having length $5ft$ and breadth $3ft$. Determine the breadth of the fencing if the length is $10ft$.

1. $6ft$
2. $5ft$
3. $4ft$
4. $15ft$

Q. The area of lllinois on the smaller map is $15$ cm${}^2.$ If the distance between Chicago and Rockford is $2$ cm on the smaller map and it is $6$ cm on the larger map, then what is the area of llinois on the larger map?

1. $115$ cm${}^2$
2. $120$ cm${}^2$
3. $125$ cm${}^2$
4. $135$ cm${}^2$

Q. Ballast tanks are used to store seawater for the functioning of a submarine. The volume of the main ballast tank of a submarine is $49m^3.$ A scale model is adopted for the submarine's design with a scale factor of $1:7.$ Find the volume of model of the main ballast tank.

1. $7m^3$
2. $\frac{1}{7}{m}^3$
3. $\frac{1}{49}{m}^3$

Q. John has a blueprint of a building which is designed with a scale factor $1:12$. The dimensions of a room in the blueprint is $10\text{in.}\times 8\text{in.}\times 12\text{in.}$
Find the actual dimension of the room.

1. $10\text{ft.}\times 8\text{ft.}\times 12\text{ft.}$
2. $120\text{ft.}\times 96\text{ft.}\times 144\text{ft.}$
3. $100\text{ft.}\times 80\text{ft.}\times 120\text{ft.}$
4. None of the above

Q.

Volume of a cuboid ------

i. $areaofbasexlength$

ii.$areaofbasexheight$

iii. $areaofbasexwidth$

Q. The area of a rectangle with dimensions $8cm\times 4cm$ is $32c{m}^2$. If the value of the scale factor is $4$, calculate the area of the larger rectangle formed by multiplying the scale factor.

1. $128c{m}^2$
2. $1024c{m}^2$
3. $512c{m}^2$
4. $256c{m}^2$