Course 1 Unit 10

Volume and Surface Area

Name: ___________________

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Lesson 10-1: Volume of Rectangular Prismsthree-dimensional (3D) figures – ______________________________________________________________________________________________________________

rectangular prism – __________________________________________________________________________________________________________________________

volume – _____________________________________________________________________________________________________________________________________

cubic units - _________________________________________________________________________________________________________________________________

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Example 1Find the volume of the rectangular prism.

V = lwh12 x ______ x ______

______ x 6=__________cm³

Got it? Find the volume of each rectangular prism.1. 2.

Example 2

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A cereal box has the dimensions shown. What is the volume of the cereal box?

V = lwh

V = 8 x 314 x 1212V = 81 x ¿¿ x ¿¿

Simplify before you multiply:V = ¿¿ x ¿¿ x ¿¿

V = ¿¿ or ________in³

Got it? 3. Find the volume of a container that measures 4 inches as its length,

5 inches high, and 812 inches wide.

Finding the HeightThe formula to find the height is this…

height= Volumelength x width

Orheight=Volume÷(length xwidth)

Example 3Find the missing dimension of the prism.

height=Volume÷(length xwidth)

h=¿÷ ¿

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h=84÷ (¿¿ )

h=¿¿

Got it? 4. Find the missing dimension of a rectangular prism with a volume of 94.5 cubic cm, a width of 7 cm, and a length of 3 cm.

5. The volume of the prism below is 960 cubic cm. Find the missing dimension of the prism.

Guided Practice:1. A rectangular kitchen sink is 25.25 inches long, 19.75 inches wide, and 10 inches deep. Find the maximum amount of water it can hold.

2. Find the missing dimension:

Volume = 126 cm3 width: 7 78 cm length: 2 cm h: ??

3. When finding the height, what formula makes the most sense to use?

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Lesson 10-2 Volume of Triangular Prismtriangular prism – __________________________________________________________________________________________________________________________

Example 1Find the volume of the rectangular prism.Find the area of the base:

A = ¿¿

2

A = ¿¿

2

A = _____V = Bh

V = 40(______)V = _________m³

Got it? Find the volume of each triangular prism.1. 2.

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Example 2A large skateboard ramp is shown. Find the volume of the triangular prism.Find the area of the triangular base.

_______ x _______ = _________________ ÷ 2 = _________

Multiply by the height:________ x 4 = _________ft³

Got it? 3. Find the volume of a triangular prism-shaped model with a base of

32 sq. cm and a height of 6 cm.

Finding the Height:Height=2 (volume )÷ (base x base height )

Or

Height= 2 (volume)(base xbase height)

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Example 3Find the height of the triangular prism.

Height=2 (volume )÷ (base x base height )

Height=2 ¿

Height=¿÷0.3

Height=¿cm

Example 4Dwane bought a cheese wedge for his March Madness party. The cheese wedge has the dimensions shown. The volume of the cheese wedge is 54 cubic inches. What is the height of the cheese wedge?

Height=2 (volume )÷ (base x base height )

He ight=2¿

Height=¿÷12

Height=¿cm

Got it? 4. Find the missing dimension of a triangular prism.

Volume = 55 km3 base length = 2 kmbase height = 5 km Height = ??

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Guided Practice: Find the volume of each prism.1. 2.

3. Derik has a triangular-shaped piece of cheesecake in his lunch. Find the volume.

Lesson 10-3: Surface Area of Rectangular Prismssurface area - _________________________________________________________

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Example 1Find the surface area of the rectangular prism.Find the area of each pair of faces.Add them up:

48 + 48 + 56 + 56 + 42 + 42 = ___________

So, the surface area is _________ sq. meters.

Got it? 1. Find the surface area of the rectangular prism.

Example 2:

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Find the surface area of the rectangular prism.Use the formula for surface area:

S.A. = 2lh + 2lw + 2hw

Front and back: Sides: Top and Bottom:2(7)(4) = 56 2(5)(4) = 40 2(5)(7) = 70

Add them up: ________ + ________ + _________ = ___________ft²

Example 3Find the surface area of the rectangular prism.

Got it?2. Find the surface area of the rectangular prism.

Example 4

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A geode is being sent in a gift box. The box measures 7 inches long, 3 inches wide, and 16 inches tall. What is the surface area of the box?

S.A. = 2lh + 2lw + 2hwS.A. = 2(_______)(_______) + 2(_______)(_______) + 2(_______)(_______)

S.A. = _______ (_______) + 14(_______) + _______ (3)S.A. = _______ + _______ + _______

S.A. = _______ sq. in.

Guided Practice:Find the surface area of each prism.1. 2.

3. How does area of a 2D shape relate to the surface area of a 3D shape?

Lesson 10-4 Surface Area of Triangular Prisms

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Example 1Find the surface area of the triangular prism. Find the area of each face and add:Triangle (x2)

1 x 0.8 = 0.8 ÷ 2 = 0.40.4 x 2 = 0.8

Rectangle (x3)2 x 1 = 22 x 3 = 6

Sum:_______ + _______ = ________ cm²

Got it? 1. Find the surface area of the triangular prism.

Example 2~ 13 ~

Find the surface area.

Break it down into its basic shapes:

Find the sum: _______ +_______+ _______ +_______ + _______ = __________m²

Got it? Find the surface area of each triangular prism.2. 3.

Example 3A bakery boxes pie pieces in a triangular prism box, as shown. Find the amount of cardboard used to make a box for a slice of pie.Add up the areas:

_______ + _______ + _______ + _______+_______

=__________in²Got it?

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4. A kaleidoscope is made of stained glass in the shape of a triangular prism. The bases are equilateral triangles. Find the surface area of the kaleidoscope.

Guided Practice:1. Find the surface area.

2. A skateboard ramp is in the shape of a triangular prism. If the entire ramp is to be painted, what is the surface area?

3. Looking at the formulas for the surface area of a rectangular prism and triangular prism, what are some similarities between the two formulas?

Lesson 10-5: Surface Area of Pyramids~ 15 ~

pyramid – _____________________________________________________________

________________________________________________________________________

lateral face – __________________________________________________________

________________________________________________________________________

slant height – _________________________________________________________

________________________________________________________________________

vertex – _______________________________________________________________

________________________________________________________________________

Example 1Find the surface area of the pyramid.

Area of the base: Area of each triangular side:7 x 7 = 49 7 x 9 = 63 63 ÷ 2 = 31.5

Find the sum:

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_______ + _______+ _______+ _______ + _______= _________cm²Got it? Find the surface area of each figure.1. 2.

Example 2Find the surface area of the pyramid.Find the area of each face and add.

Area of base: _______ x _______÷ 2 = _______Area of lateral faces: _______ x _______ ÷ 2 = 10

Sum: _______ + _______ + _______ + _______ = __________ft²

Got it? Find the surface area of each pyramid.3. 4.

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Example 3A pyramid puzzle has all sides that are equilateral triangles. Each triangle has side lengths of 8 centimeters. The slant height is 6.9cm. Find the surface area of the puzzle.Each face has an area of

_______ x _______÷ 2 = _______

So the surface area is 4 x __________

or __________ cm2

Got it? 5. Pyramid-shaped gift boxes have square bases that measure 5 inches on each side. The slant height is 6.5 inches. How much cardboard is used to make each box?

Guided Practice:Find the surface area of each pyramid. 1. 2. 3.

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