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2.04 Interpret plans, elevations and architectural drawings

Worksheet
Dimensions in 3D drawings
1

Consider the given diagram:

a

Find the dimension indicated by A.

b

Find the dimension indicated by B.

2

Given the following diagram:

a

Find the dimension indicated by X.

b

Find the dimension indicated by Y.

c

Find the dimension indicated by Z.

Plan and elevation views
3

Consider the following figure:

a

State whether the following figures are identical to the original figure:

i
ii
iii
iv
b

If the side of each single cube measures 3 \text{ cm}, find the height, width and length of the original figure.

c

The figure to the right is a prism. How many cubes would need to be removed from it to form the original figure that was given?

4

Consider the following figure:

a

State whether the following figures are identical to the original figure:

i
ii
iii
iv
b

If the side of each cube measures 5 \text{ cm}, find the height, width and length of the original figure.

c

The figure to the right is a prism. How many cubes would need to be removed from it to form the original figure that was given?

5

Consider the following figure:

a

State whether the following figures are identical to the original figure:

i
ii
iii
iv
b

If the side of each cube measures 4 \text{ mm}, find the height, width and length of the original figure.

c

The figure to the right is a prism. How many cubes would need to be removed from it to form the original figure that was given?

6

Consider the following figure:

a

State whether the following figures are identical to the original figure:

i
ii
iii
iv
b

If the side of each cube measures 4 \text{ mm}, find the height, width and length of the original figure.

c

When comparing the object to the following solid, how many cubes have been cut away?

7

Consider the following object:

a

If the length of the front face of the object is 24 \text{ m}, what is the length X of each of the boxes on the front face?

b

What is the maximum height of the object?

Scale drawings
8

On a house plan that has been drawn to a scale of 1:100, the building is drawn to a length of 158 \text{ mm}. Find the actual length of the building in metres.

9

A scale model for a new skyscraper has been constructed and has model windows that are 1.54 \text{ cm} wide. The actual windows will be 5.5 \text{ m} wide. What ratio is the model using?

10

Given below is the plan for Neil's new house. All measurements are in millimetres.

a

What do the following symbols represent on the house plan?

i
ii
iii
iv
v
vi
vii
viii
b

Which room has dimensions 3600 \times 3150?

c

How many outward windows does this house have?

d

If Neil looks out the window of bedroom 1, what direction will he be looking?

e

If Neil looks out the window of the garage, what direction will he be looking?

f

In what direction do the garage doors face?

g

Find the dimensions of the garage (in metres).

h

If the cost of flooring 1 \text{ m}^{2} is \$588, how much will it cost to floor the garage?

11

Consider the following floor plan. All measurements are in metres.

a

Find the dimensions of the family room (in millimetres).

b

How many toilets are there?

c

Where are the 2 linen presses?

d

State the meaning of:

i

BTH

ii

Robe

iii

SHR

iv

ref

e

How many doors are inside the house?

f

Which bedroom is the smallest?

g

Which is bigger, the media room or the family room? By how many square metres?

12

For the house floor plan below:

a

Use the scale to find the width (horizontal) and length (vertical) of the kitchen.

b

Calculate the total floor area of the house.

13

Bart and Deborah are buying a house with the following floor plan:

a

What is the thickness of the external walls?

b

What is the thickness of the internal walls?

c

What is the total width of the house in metres?

d

What is the total length of the house in metres?

e

Find the dimensions of the the Family Room (in millimetres).

14

Consider the given floor plan:

a

According to the scale of the diagram, 1 \text{ cm} on the diagram represents how many metres in the house?

b

Using a ruler, Neville measures the length of Bed 1 on the plan and finds it to be 4 \text{ cm}. How many metres does this represent?

c

Using a ruler, Neville measures the width of Bed 1 on the plan and finds it to be 8 \text{ cm}. How many metres does this represent?

d

Neville wants to tile the floor of Bed 1. If each tile is 20 \text{ cm} by 10 \text{ cm}, how many tiles would Neville need?

e

If each tile weighs 200 \text{ g}, calculate the total weight of the tiles in grams.

f

Due to building regulations the total weight of the tiles cannot be more than 325 \text{ kg}. Convert your answer from part (e) to kilograms and determine if Neville will be able to use these tiles on the floor.

15

Consider the following floor plan:

a

How many bedrooms does this house have?

b

How many of the bedrooms have built-in wardrobes?

c

Does this house have an ensuite bathroom?

d

Find the dimensions of the family room.

e

What bedroom has the largest floor area?

f

The floor area of the house is 128 \text{ m}^{2}. Calculate the cost of building the floor for this house at a rate of \$630 per square metre.

16

The following is a 1:200 floor plan of a house. The homeowner wishes to add a dining room table, which is 150\text{ cm} long, placing it where the \times is marked on the floor plan.

Find the length of the table that should be drawn to in the floor plans.

17

A plan of a building with ratio 1:90 is enlarged so its length and width are both doubled as shown:

a

Find the new scale ratio for the larger plan.

b

The scale bar on the original plan represents 5\text{ m}. When the plan is doubled, the scale bar is doubled as well. Find the length that the new scale bar represents.

18

An architect is designing a house that is 21 \, \text{m} long and 15 \,\text{m} wide.

a

She wants to print the plans for this house in a 84 \, \text{cm} by 60 \,\text{cm} section of a large piece of paper. Find the ratio she should use to fit the plans on the paper.

b

After printing the plans, the architect measures the length of the hallway to be 24 \, \text{cm} on paper. She wants to order a rug that covers the full length of the hallway.

How long should the rug be in metres?

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Outcomes

3.2.4

interpret commonly used symbols and abbreviations in scale drawings

3.2.5

determine actual measurements of angle, perimeters and areas from scale drawings

3.2.6

estimate and compare quantities, materials and costs using actual measurements from scale drawings, for example using measurements for packaging, clothes, painting, bricklaying and landscaping

3.2.7

understand and apply drawing conventions of scale drawings, such as scales in ratio, dimensions and labelling

3.2.9

interpret plans and elevation views of models

3.2.10

sketch elevation views of different models

3.2.11

interpret diagrams of three-dimensional objects

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