3D Shapes Volume and Surface Area

3-D Shapes

An Introduction to Surface Area and Volume

Symbols used in this unit

Common Formula

take a picture of these formulas or google "Geometric Formulas"

Note: B = base Area and b = length of the base of an object

Multiple Choice

$$A=\frac{bh}{2}$$  where b is the base (that the height touches) and h is the height 

What is the Area of a triangle? 

• 20 cm²

• 56 cm²

• 28 cm²

• 27 cm²

Multiple Choice

$$A=\ bh$$  where b= base and height is the perpendicular distance from base to opposite side.

What is the area of this parallelogram?

• 75 square cm

• 35 square cm

• 15 square cm

• 105 square cm

Multiple Choice

$$A\ =\ \frac{h\left(b_1+b_2\right)}{2}$$  where b are the parallel bases. 

Find the area of the trapezoid.

• 18 m²

• 165 m²

• 84 m²

• 22.5 m²

Multiple Choice

What is the area of this circle? $$A=\pi r^2$$  where r is the radius and the radius is half the diameter and use  $$\pi$$  on demos calculator (3.14) 

• 163.2

• 15.3

• 124.2

• 113.1

Multiple Choice

Calculate the volume.  To find the volume find the area of the triangle base and multiply by the height of the figure.  $$V=Bh,$$  where B is area of triangle, h is length of rectangle. 

•  90 cm³

• 150 cm³

• 180 cm³

Multiple Choice

$$V=lwh$$  in this figure  $$l=12,\ w\ =5.1,\ h\ =7$$  

 Find the Volume

• 428.4 cm³

• 412.8 cm³

• 404.2 cm³

• 400 cm³

Multiple Choice

$$SA\ =\ 2lw+2lh\ +2wh$$  In this figure  $$l=15,\ w=10,\ h=10$$   What is the surface area of this figure?

• 200 cm ²

• 800 cm ²

• 400 cm ²

• 100 cm ²

Multiple Choice

$$S.A.=hp\ +2B$$  in this firgure h=8, p=perimeter of triangle and B= area of triangle base. 

Find the total surface area of the prism.

• 161 square feet

• 1,700 square feet

• 75 square feet

• 186 square feet

Solid Figures

Cylinder, Sphere, Cone, Pyramid

Multiple Select

$$S.A.\ =\ 2\pi r^2+2\pi rh$$  in this picture  $$r=4,\ h\ =11$$  

What is the surface area of the cylinder?

• 176π cm²

• 376.8 cm³

• 376.8 cm²

• 120π cm²

Multiple Choice

$$S.A.=\frac{1}{2}lp+B$$ in this picrture $$l\$$  = 4 (height of triangle face), p = 4(2)= pereimeter of square base, B=2(2) = area of the square base. 

Find the Surface Area

• 15m²

• 16m²

• 18m²

• 20m²

Multiple Choice

$$S.A.\ =\ \pi rl$$  

If slant height,  $$l$$ , of the cone is 21 cm and the diameter (2r) of the base is 24 cm. The total surface area of a cone is:

• 1200.77 sq.cm

• 1177 sq.cm

• 1222.77 sq.cm

• 1244.57 sq.cm

Multiple Choice

$$S.A.=4\pi r^2$$  The surface area of a sphere of radius 14 cm is:

• 1386 sq.cm

• 1400 sq.cm

• 2464 sq.cm

• 2000 sq.cm

Multiple Choice

$$S.A.=\frac{1}{2}\left(4\pi r^2\right)$$  

Find the surface area of the hemisphere (half a sphere)

• 339.3 in²

• 226.1in²

• 113.0 in²

• 452.2 in²

This concludes a summary of Surface Area and Volume

Please ask questions to help you understand. Please use DESMOS calcultor to help the calculations. Refer to the lesson Plan for more practice.

Multiple Choice

Find the area of the composite figure.

• 100

• 400

• 137.5

• 175

Multiple Choice

Determine the area of the composite figure shown below.

• 168 centimeters squared 

• 98 centimeters squared 

• 84 centimeters squared 

• 70 centimeters

Multiple Choice

The area of the base of this trapezoidal prism is 15 square units. What is the volume?

• 120 units³

• 120 units²

• 15 units³

• 240 unit³

Multiple Choice

A square pyramid is covered with decorative wrapping paper with no overlap.  The net of the box is shown on the right.  How many square centimeters of wrapping paper are needed to cover the surfaces of the box? 

• 108 cm²

• 324 cm²

• 180 cm²

• 432 cm²

Multiple Choice

Calculate the surface area of the square pyramid.

• 228 m²

• 144 m²

• 300 m²

• 156 m²

Parts of a 3D figure

• Faces: flat sides

• Edges: lines in between 2 faces

• Vertices: corners or points where edges connect

Multiple Choice

How many faces?

• 2

• 4

• 6

• 8

Multiple Choice

The corners or points on a 3D object are called...

• outlines
• cylinder
• lines
• vertices

We're going to look at 2 shapes:

Prisms and Pyramids

Prisms:

• TWO parallel bases

• Rectangular faces

• Names come from the bases

• Example: The triangular prism has two triangle bases

Multiple Choice

A prism gets its name from its

• faces

• bases

Multiple Choice

The base of a triangular prism is a

• square

• triangle

• rectangle

Pyramids:

• 1 base

• Triangular faces

• Names come from the bases

• Example: The square pyramid has one square base

Multiple Choice

Both prisms and pyramids are named for their

• vertices

• edges

• base(s)

• faces

Multiple Choice

A pyramid has _______ base(s).

• 1

• 2

Multiple Choice

The base of a square pyramid is a

• square

• triangle

• hexagon

Nets

• Nets are the unfolded version of a 3d figure.

• A net shows you all the different faces and base(s)

• We can use nets to help us calculate surface area

Multiple Choice

This is a net of what shape?

• Cube

• Rectangular Prism

• Triangular Prism

• Square Pyramid

Multiple Choice

What is a net?

• A flattened three-dimensional figure

• A two-dimensional shape

• The formula for volume

• The formula for area