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E. Spatial Sense · Spatial Sense: 3D Objects, Transformations, Circles, Surface Area and Volume

Spatial Sense: 3D Objects, Transformations, Circles, Surface Area and Volume: Unit Review

A1 E1.1 E1.2 E1.3 E1.4 E2.1 E2.2 E2.3 E2.4 E2.5 E2.6 E2.7About 40 minutes
Learning goals
  • I can classify prisms, pyramids and cylinders, including their symmetry, and draw views to scale.
  • I can perform dilations and describe translations, reflections and rotations with coordinates.
  • I can explain volume and capacity and convert metric units of length, area and volume.
  • I can find the circumference and area of circles, construct circles, and find the surface area and volume of prisms and cylinders.

Words to know

plane of symmetry
A plane that cuts a 3D object into two mirror-image halves.
scale
A ratio comparing drawing lengths with real lengths, like 1 cm : 50 cm.
dilation
A transformation that enlarges or reduces a shape by a scale factor, giving a similar shape.
1 cm³ = 1 mL
The link between volume and capacity.
π
Circumference ÷ diameter for any circle, about 3.14.
V = B × h
Volume of a prism or cylinder: area of base × height.

Let's review!

In this unit you classified prisms, pyramids and cylinders and found their planes and axes of symmetry, drew views to scale, performed dilations, described transformations with coordinate rules, compared volume and capacity, converted metric units of area and volume, discovered π, constructed circles, found the area of a circle, and found the surface area and volume of cylinders and prisms.

This review has a few questions from every lesson. Use π ≈ 3.14. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

rrd = 2 × rCircumference (around)C = π × d = 2 × π × rArea (inside)A = π × r × rCylinder volumeV = π × r × r × h
The circle formulas from this unit, with π ≈ 3.14. Area and volume use r × r, so their units are squared (cm²) and cubed (cm³).
translationreflectionrotation 90°dilation ×2
Four transformations of a flag: the original is solid and the image is dashed. The first three make congruent images; a dilation makes a similar image.

Classifying Prisms, Pyramids and Cylinders

1

How many faces, edges and vertices does a hexagonal pyramid have?

2

A prism has 18 edges. What shape is its base?

3

What is the difference between a right prism and an oblique prism?

Plane Symmetry and Rotational Symmetry of 3D Objects

1

How many planes of symmetry does a right square pyramid have?

2

What is the order of rotational symmetry of a right pentagonal prism (regular base) around the axis through its bases? What is the smallest angle of turn?

3

How many planes of symmetry does a right triangular prism with an equilateral base have?

Views, Perspective Drawings and Scale

1

At a scale of 1 cm : 50 cm, how long is a 4 m wall on the drawing?

2

At a scale of 1 cm : 2 m, a drawing line is 6.5 cm. How long is the real object?

3

A box is 40 cm long, 30 cm wide and 20 cm tall. What size is its top view at 1 cm : 10 cm?

Dilations and Similar Shapes

1

Dilate (4, 6) with the origin as centre and scale factor 1/2.

2

A 5 cm side becomes 20 cm after a dilation. What is the scale factor?

3

Are triangles with sides 4, 6, 8 and 6, 9, 12 similar?

Transformations on the Cartesian Plane

1

Reflect (3, −5) in the y-axis.

2

Rotate (4, 1) 90° counterclockwise about the origin.

3

Write the rule for the translation that moves (2, −1) to (−3, 2).

4

Reflect (1, 6) in the line y = 2.

Volume and Capacity

1

750 cm³ = ? mL

2

What is the capacity, in litres, of a container whose inside is 20 cm by 10 cm by 15 cm?

3

Water rises from 250 mL to 290 mL when a toy is added. What is its volume?

Converting Units for Perimeter, Area and Volume

1

5 m² = ? cm²

2

A floor is 350 cm by 400 cm. What is its area in m²?

3

A box is 50 cm by 40 cm by 30 cm. What is its volume in m³?

Radius, Diameter and Circumference

1

Find the circumference of a circle with a diameter of 12 cm.

2

Find the circumference of a circle with a radius of 2.5 m.

3

A circle has a circumference of 94.2 cm. What is its radius?

Constructing Circles

1

To construct a circle with a diameter of 7 cm, what width do you set the compass to?

2

What radius do you use to construct a circle with a circumference of 37.68 cm?

3

How can you draw a circle with a radius of 1 m on a driveway?

The Area of a Circle

1

Find the area of a circle with a radius of 6 cm.

2

Find the area of a circle with a diameter of 20 m.

3

A circle has an area of 28.26 cm². Find its radius.

4

Find the area of a semicircle with a radius of 2 cm.

Nets and Surface Area of Cylinders

1

Find the surface area of a closed cylinder with r = 2 cm and h = 3 cm.

2

A label covers the curved side of a can with d = 10 cm and h = 12 cm. What is its area?

3

A cylinder net's rectangle is 31.4 cm long. What is the radius of the cylinder?

Volume of Prisms and Cylinders

1

Find the volume of a cylinder with r = 3 cm and h = 5 cm.

2

A triangular prism has a triangle with base 8 cm and height 5 cm, and is 12 cm long. Find its volume.

3

A prism has V = 480 cm³ and h = 12 cm. Find its base area.

Just for fun

Why was the circle such a good study buddy for this review?

It had already gone around every topic once.

How to use this review

  • Do one section at a time. Write your work on paper and show each step.
  • Use π ≈ 3.14 and a calculator for long multiplication if your grown-up says it's OK. The thinking matters most.
  • Check units: lengths in cm, areas in cm², volumes in cm³.
  • If you miss two or more questions in a section, go back to that lesson and redo its Your turn questions.
  • Finish with the quiz below.
Check your understanding

Quiz

1.

How many edges does a pentagonal prism have?

2.

How many planes of symmetry does a cube have?

3.

At a scale of 1 cm : 20 cm, how long is a real 2 m couch on the drawing?

4.

Dilate (2, 5) with the origin as centre and scale factor 3.

5.

Rotate (2, 3) 180° about the origin.

6.

A box measures 10 cm by 5 cm by 4 cm inside. What is its capacity?

7.

2 m² = ?

8.

What is the circumference of a circle with a radius of 5 cm?

9.

What is the area of a circle with a diameter of 10 cm?

10.

What is the volume of a cylinder with r = 2 cm and h = 5 cm?

For parents and teachers

Using this review: Let your child work through one section at a time and check their own answers. Then look at which sections caused trouble:

  • Miscounting faces, edges or vertices, or mixing up prisms and pyramids → revisit Classifying Prisms, Pyramids and Cylinders.
  • Wrong number of planes of symmetry or wrong order of rotation → revisit Plane Symmetry and Rotational Symmetry of 3D Objects (use real objects and a mirror).
  • Scale mistakes or mismatched views → revisit Views, Perspective Drawings and Scale.
  • Adding instead of multiplying in a dilation, or calling non-similar shapes similar → revisit Dilations and Similar Shapes.
  • Mixing up reflection or rotation rules → revisit Transformations on the Cartesian Plane.
  • Confusing volume and capacity, or 1 cm³ = 1 mL → revisit Volume and Capacity.
  • Converting m² to cm² by 100 instead of 10 000 → revisit Converting Units for Perimeter, Area and Volume.
  • Mixing up radius and diameter in C = π × d → revisit Radius, Diameter and Circumference.
  • Setting the compass to the diameter → revisit Constructing Circles.
  • Using the diameter in π × r × r, or confusing area with circumference → revisit The Area of a Circle.
  • Wrong rectangle length or wrong number of circles in a net → revisit Nets and Surface Area of Cylinders.
  • Forgetting ÷ 2 for triangles, or mixing up the two heights → revisit Volume of Prisms and Cylinders.

Celebrate how much your child has learned: this unit connects shapes, transformations and measurement in ways they'll use in Grade 8 and beyond.