Scale Factor

Q.

The dimensions of a book are measured in centimeters while the dimensions of a room are measured in meters. Explain?

Q. The distance between school and house of a girl is given by 5 cm in a picture, using the scale 1 cm : 5 km. Find the actual distance between the two places?

Q. Using the given triangle, calculate the height and base of a triangle with scale factor $4$.

1. $b=45,h=24$
2. $b=60,h=24$
3. $b=60,h=32$
4. $b=45,h=32$

Q.

The bar graph given alongside shows the number of visitors visited a historical place from March to July. Read the bar graph and answer the following question:

What is the percentage change in the number of visitors in the last two months from first three months?

Q.

Read the given bar graph.

i) What information does the bar graph convey?

ii) What is the scale of this graph?

iii) How many more apples were grown on$T7$ than on$T1$?

iv) How many fewer apples were grown on $T1$than on $T6$?

Q. Figure B is a blueprint image of figure A. Find the value of $x$ using the dimensions given in the diagram.

1. $4$ units
2. $6$ units
3. $8$ units
4. $12$ units

Q.

The following bar graph shows the number of people who visited the ‘TAJ MAHAL’ over a period of 5 months. Use the graph to answer how many visitors were there in 5months?

Q.

A survey regarding the heights (in cm) of $50$ boys of a class was conducted and the following data was obtained.

Height (in cm)	$140-145$	$145-150$	$150-155$	$155-160$	$160-165$	$165-170$	$170-175$
No. of boys	$12$	$10$	$8$	$9$	$6$	$4$	$1$

Draw both the ogives for the above and hence obtain the median height of the students.

Q. Square $ABCD$ is dilated about the origin. If the scale factor is $0.5$, what are the coordinates of the resultant image $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ ?

1. $A^{\prime }(0.5,0.5),B^{\prime }(1.5,0.5),C^{\prime }(1.5,1.5),D^{\prime }(0.5,1.5)$
2. $A^{\prime }(2,2),B^{\prime }(6,2),C^{\prime }(6,6),D^{\prime }(2,6)$
3. $A^{\prime }(0.25,0.25),B^{\prime }(1.5,0.25),C^{\prime }(1.5,1.5),D^{\prime }(0.25,1.5)$
4. $A^{\prime }(3,3),B^{\prime }(1.5,3),C^{\prime }(1.5,1.5),D^{\prime }(3,1.5)$

Q. The dimensions of a room is $10ft\times 8ft\times 8ft$. Calculate the value of the scale factor if the dimensions of the scale model is $20in\times 16in\times 16in$.

1. $\frac{1}{12}$
2. $\frac{1}{6}$
3. $\frac{1}{24}$
4. $\frac{1}{2}$

Q.

The chart shows the number of sunny days and the number of windy days in six months. Which months had more windy days than sunny days?

1. MAY

2. JUNE

3. AUG

4. OCT

Q.

This bar graph shows the number of gold medals won by $4$ countries in an event. Use the graph to answer how many more gold medals did D win than C?

Q. In a model of a soccer field, the length of the field is $10\text{inches}.$ If the actual length of the football field is $100\text{yards},$ find the scale factor used to draw the model.

1. $\frac{1}{10}$
2. $\frac{1}{360}$
3. $\frac{1}{3600}$
4. None of the above

Q. A small aeroplane has a wing span of $15\text{feet}.$ The scale factor for a model of the aeroplane is $\frac{1}{60}$. Find the wing span of the model in inches.

1. $2$
2. $3$
3. $4$
4. $6$

Q. The indicates the amount by which an object is enlarged or reduced.

Q. Area of a right triangle ABC is 120 sq feet. If ΔABC goes through a dilation transformation with a scale factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?

1. 220 sq feet
2. 360 sq feet
3. 270 sq feet
4. 480 sq feet

Q. The actual distance between two cities is $5km$, if the scale factor is $1:100,000$, the distance (in $cm)$ on the map is

1. $50cm$
2. $5cm$
3. $500cm$
4. $10cm$

Q. Actual distance is calculated by dividing the distance given on the map by the scale factor.

1. True
2. False

Q.

From the bar graph shown below, find how many workers are of age 18 years or below?

1. 18

2. 12

3. 20

4. 13

Q. The actual distance between New Jersey and New York is $70$ miles while the distance on the map is $7$ inches. Calculate the scale factor.

1. $\frac{1}{4900}$
2. $\frac{1}{49,000}$
3. $\frac{1}{633,600}$
4. $\frac{1}{63,360}$

Q. If a rectangle goes through a reflection, clockwise rotation of ${90}^o$, and then dilation with a scale factor of 5, then what will be the ratio of the area of the preimage to the area of image?

1. 0.04
2. 25
3. 0.05
4. 1/2

Q.

The side of a square board is $50\mathrm{cm}.$ A student has to draw an image in her notebook. If the drawing of the square board in the notebook has a perimeter of $40\mathrm{cm},$ then by which scale the figure has been drawn?

Q. What will be the side length of a regular pentagon if it goes through a dilation transformation with a scale factor of 2.8? The side length of the preimage is 8 units.

1. 18.6 units
2. 20.6 units
3. 24.6 units
4. 22.4 units

Q.

There are 3 cab companies A, B and C. They provide cab service at different time slots. The time taken for the trip depends upon the driver skill. The bar graph shown below gives the details.

Suppose you have to reach your class as early as possible before 10 am. Which of the cabs will you choose and which time slot?

1. Company C, C3, 10-11

2. Company B, C1, 8-9

3. Company A, C2, 9-10

4. Company C, C1, 8-9

Q. The dimensions of a cuboid is $10cm\times 8cm\times 5cm$. Calculate the volume of the new cuboid if the scale factor is $0.5$.

1. 50

Q.

Read the bar graph (Figure) which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:

About how many books were sold in $ 1989, 1990 \mathrm{and} 1992 ?$

Number of books 600 500 400 300 200 100 Scale: 1 unit =100 books 

Q. How many school teachers does each smile represent?

1. 500
2. 400
3. 700
4. none of these

Q.

There are 3 cab companies A, B and C. They provide cab service at different time slots. The time taken for the trip depends upon the driver skill. The bar graph shown below gives the details.

Suppose you have to reach your class as early as possible before 10 am. Which of the cabs will you choose and which time slot?

1. Company A, C2, 9-10

2. Company B, C1, 8-9

3. Company C, C1, 8-9

4. Company C, C3, 10-11

Q. In $△ABC,AB=BC=6$ cm. $A$ circle is drawn with the center at $B$ and a radius of $2$ centimeters. What is the scale factor of the triangle formed by the point $B$ and the points where the circle intersects $△ABC$?

1. $1$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{1}{2}$

Q. The two-dimensional drawings that are proportional to the size of the actual object are known as -

1. sketches
2. drawings
3. scale drawings
4. None of the above.