#### Solved Examples and Worksheet for Scale Drawings

Q1The actual length of a film is 0.9 inches and the length, after projecting it on to the screen, is 3 inches. Find the scale factor of the projector.

A. 4.3
B. 4.6
C. 3.8
D. 3.3

Step: 1
Scale factor = (length after projection) / (actual length)
Step: 2
= 30.9 = 3.3
[Substitute the values and simplify.]
Step: 3
The scale factor of the projector is 3.3.
Q2The height of the Grad school logo is 12 in. The administration of the school is planning to enlarge the logo so that the height of the logo should be 15 in. Find the scale factor.
A. 2.25
B. 1
C. 1.75
D. 1.25

Step: 1
Scale factor = (height of the enlarged logo) / (actual height of the logo)
= 1512 = 54 = 1.25
[Simplify.]
Step: 2
The scale factor is 1.25.
Q3A model of a dinosaur skeleton was made using a scale of 1 ft : 15 ft in a museum. If the size of the dinosaur's tail in the model is 8 ft, then find its actual length.

A. 140 ft
B. 130 ft
C. 110 ft
D. 120 ft

Step: 1
Let, n be the actual size of the dinosaur's tail.
Step: 2
115 = 8n
[The dimensions of the actual dinosaur will be in proportion to the dimensions of the model.]
Step: 3
n × 1 = 8 × 15
[Write the cross products.]
Step: 4
n = 120
[Simplify.]
Step: 5
So, the actual size of the dinosaur's tail is 120 ft.
Correct Answer is :   120 ft
Q4The scale of the picture shown is 1 cm : 1 in. Find the actual height of the cup. A. 2 in
B. 3 in
C. 1 in
D. 4 in

Step: 1
Let m be the actual height of the cup.
Step: 2
11 = 2m
[Write the proportion.]
Step: 3
m × 1 = 1 × 2
[Write the cross products.]
Step: 4
m = 2
[Simplify.]
Step: 5
The actual height of the cup is 2 in.
Correct Answer is :   2 in
Q5The scale of the picture shown is 1 inch : 20 cm. What is the actual height of the penguin? A. 56 cm
B. 68 cm
C. 64 cm
D. 60 cm

Step: 1
Let p be the actual height of the penguin.
Step: 2
120 = 3p
[Write the proportion.]
Step: 3
p × 1 = 20 × 3
[Write the cross products.]
Step: 4
p = 60
[Simplify.]
Step: 5
The actual height of the penguin is 60 cm.
Correct Answer is :   60 cm
Q6Length of a lake is 5 inches on map. The map of the lake has a scale of 1 inch : 20 miles. Find the actual length of the lake.
A. 150 miles
B. 50 miles
C. 80 miles
D. 100 miles

Step: 1
Let k be the actual length of the lake.
Step: 2
120 = 5k
[Write the proportion.]
Step: 3
k x 1 = 5 x 20
[Write the cross products.]
Step: 4
k = 100
[Multiply.]
Step: 5
The actual length of the lake is 100 miles.
Correct Answer is :   100 miles
Q7A bridge was supposed to be built across a river and the architect drew a 3 cm long bridge using a scale 1 cm : 3 miles on paper. Find the actual length of the bridge.
A. 11 miles
B. 10 miles
C. 12 miles
D. 9 miles

Step: 1
Let b be the length of the bridge.
Step: 2
13 = 3b
[Write the proportion using the scale.]
Step: 3
b x 1 = 3 x 3
[Write the cross products.]
Step: 4
b = 9
[Multiply.]
Step: 5
The length of the bridge is 9 miles.
Correct Answer is :   9 miles
Q8A Botany student drew a sketch of a plant, using a scale of 1 inch : 3.3 ft. Find the actual height of the plant, if the sketch is 2 in. long.
A. 5.6 feet
B. 6.3 feet
C. 6.6 feet
D. 7.6 feet

Step: 1
Let n be the actual height of the plant.
Step: 2
13.3 = 2n
[Write the proportion using the scale.]
Step: 3
n x 1 = 2 x 3.3
[Write the cross products.]
Step: 4
n = 6.6
[Multiply.]
Step: 5
The actual height of the plant is 6.6 feet.
Correct Answer is :   6.6 feet
Q9Scale of the couch shown is 1 inch : 12 feet. Find the actual height of the couch, if the height of the couch in the picture is 4 inches. A. 4 feet
B. 3 feet
C. 2 feet
D. None of the above

Step: 1
Let h be the actual height of the couch.
Step: 2
1/ = 4/h
[Write the proportion using the scale.]
Step: 3
h x 1 = 4 x 12
[Write the cross products.]
Step: 4
h = 2
[Multiply.]
Step: 5
The actual height of the couch is 2 feet.
Correct Answer is :   2 feet
Q10A model baseball bat was placed at the entrance of a stadium, which measured 13 feet in length. A scale of 1 foot : 2 inches is used for the model. Find the actual length of the bat.

A. 27 inches
B. 26 inches
C. 29 inches
D. 25 inches

Step: 1
Let n be the actual length of the bat.
Step: 2
12 = 13n
[Write the proportion.]
Step: 3
n × 1 = 2 × 13
[Write the cross products.]
Step: 4
n = 26
[Simplify.]
Step: 5
The actual length of the bat is 26 inches.
Correct Answer is :   26 inches
Q11A remote sensing map shows that 12 square inches of land is submerged in water due to floods. Find the actual area submerged in water, if the scale of the map is 1 square inch : 12 square miles.
A. 149 square miles
B. 139 square miles
C. 129 square miles
D. 144 square miles

Step: 1
Let n be the actual area of the land submerged in water.
Step: 2
112 = 12n
[Write the proportion.]
Step: 3
n x 1 = 12 x 12
[Write the cross products.]
Step: 4
n = 144
[Simplify.]
Step: 5
The actual area of the land submerged in water is 144 square miles.
Correct Answer is :   144 square miles
Q12A botany student drew a sketch of a tree using a scale of 1 inch : 4 meters. Find the actual height of the tree, if it measures 4 inches in the sketch.

A. 19 meters
B. 15 meters
C. 4 meters
D. 16 meters

Step: 1
Let n be the actual height of the tree.
Step: 2
14 = 4n
[Write the proportion.]
Step: 3
n × 1 = 4 × 4
[Write the cross products.]
Step: 4
n = 16
[Simplify.]
Step: 5
The actual height of the tree is 16 meters.
Correct Answer is :   16 meters
Q13An 105 ft tall statue was carved and the sculptor used a 15 in. sketch of the statue as a blueprint. What scale did the sculptor use?

A. 1 in. : 1 ft
B. 1 in. : 7 ft
C. 3 in. : 7 ft
D. 2 in. : 6 ft

Step: 1
The scale is the ratio of size of the statue in the blue print to the size of the original statue.
Step: 2
15105
[Write the ratio.]
Step: 3
= 15÷15105÷15 = 17
[Divide both numerator and denominator by the GCF 15.]
Step: 4
The scale used by the sculptor is 1 in. : 7 ft.
Correct Answer is :   1 in. : 7 ft
Q14The height of a tree in a picture was 2 in. Find the actual height of the tree, if the scale of the picture was 1in : 9 m.
A. 18 meters
B. 20 meters
C. 16 meters
D. 9 meters

Step: 1
Let n be the actual height of the tree.
Step: 2
1in.9m = 2in.n
[Write the scale and its related Proportion.]
Step: 3
n x 1 = 2 x 9
[Write the cross products.]
Step: 4
n = 18
[Multiply.]
Step: 5
So, the actual height of the tree is 18 meters.
Correct Answer is :   18 meters
Q15Jason wanted to draw a picture of a 64 m tall transmitting tower on a hillock of height 160 m. The combined length of the hillock and the tower on the paper is 7 cm. Find the scale Jason used.

A. 2 cm : 32 m
B. 1 cm : 32 m
C. 1 m : 32 cm
D. 2 m : 32 cm

Step: 1
The actual combined length of hillock and tower = 160 + 64 = 224 m
Step: 2
7224
[(length of the model)/(actual length)]
Step: 3
= (7÷7)(224÷7) = 132
[Divide both numerator and denominator by the GCF 7.]
Step: 4
Jason used a scale of 1 cm : 32 m.
Correct Answer is :   1 cm : 32 m