Surface Area and Volume of Rectangular Prisms and Cylinders

Surface Area

&

Volume

By Ms. Martinez

Volume of a Cylinder

​V=πr²h

π - use pi button or 3.14

r - radius or diameter/2

h- height​

Volume of a Cylinder

v=πr²h

v = (3.14)(6.5)²(4.5)

v=​597.3 ft²

​1. Find the volume of the cylinder.Round to the nearest tenth. Use 3.14.

Volume of a Cone

​V=⅓πr²h

π - use pi button or 3.14

r - radius or (diameter/2)

h- height​

Volume of a Cone

v=⅓πr²h

v = ⅓(3.14)(4)²(12)

v=​201.06 in²

​1. Find the volume of the cone. Round to the nearest tenth. Use 3.14.

r = d/2

r=8/2

r= 8 in​

Volume of a Sphere

​V=4/3πr³

π - use pi button or 3.14

r - radius or (diameter/2)

Volume of a Cone

v=4/3πr³

v =4/3(3.14)(8)²

v=​2144.66 m

​1. Find the volume of the sphere. Round to the nearest tenth. Use 3.14.

Surface Area of a Rectangular Prism

​Get the area of each side and add them.

A(area) = L*W

Surface Area of a Rectangular Prism

A(area) = L*W

A​, side 1 = L*H, 4*5 = 20 in

A​, side 2 = W*H, 3*5 = 15 in

A​, side 3 = L*W, 4*3 = 12 in​

A​, side 4 = L*H, 4*5 = 20 in​

A​, side 5 = W*H, 3*5 = 15 in​

A​, side 6 = L*W, 4*3 = 12 in​

​

S = ​20 + 15 + 12 + 20 + 15 + 12 = 94 in²

Lateral Surface Area of a

Rectangular Prism

Add only the 4 sides that are the same size.

A(area) = L*W

A​, side 1 = L*H, 4*5 = 20 in

A​, side 2 = L*W, 4*3 = 12 in

A​, side 3 = L*H, 4*5 = 20 in​

A​, side 4 = L*W, 4*3 = 12 in

​

L =20 + 12 + 20 + 12 = 64 in² ​

Surface Area of a Triangular Prism

​Total Surface Area - Get the area of each side and add them.

​Lateral Surface Area - Get the area of only the rectangle sides and add them.

Total Surface Area

​A of triangle - (L*W)/2

A of triangle - (5*6)/2 = 15​

A of Side 1 - 8*5 = 40

A of Side 2 - 8*6 = 48

A of Side 3 - 8*5 = 40

​

S = 15 + 40 + 48 + 40 +15

=158 cm²​

Method 1

Method 2

S = ph +2B

P, perimeter = 5+5+6= 16

h, height = 3

B, area of base = (3*6)/2

​

S = 16(3) + 2 ((3*6)/2)​

= 66 cm²​

3 cm​

Lateral Surface Area

​A of triangle - (L*W)/2

A of triangle - (5*6)/2 = 15​

A of Side 1 - 8*5 = 40

A of Side 2 - 8*6 = 48

A of Side 3 - 8*5 = 40

​

S = 15 + 40 + 48 + 40 +15

=158 cm²​

Method 1

Method 2

S = ph +2B

P, perimeter = 5+5+6= 16

h, height = 3

B, area of base = (3*6)/2

​

S = 16(3) + 2 ((3*6)/2)​

= 66 cm²​

3 cm​

Surface Area of a Cylinder

​L, Lateral = 2πrh

S, Total = 2π​r² + 2πrh

Total surface area is also 2π​r² + Lateral

​

r = radius

h = height

d= diameter/2 = radius​

Lateral Surface Area

​L, Lateral = 2πrh

L = 2πrh

L = 2(3.14)(3)(9)

L = 169. 56 in²​

​

Use 3.14 for π

​

R = Radius = 3

H = Height = 9​

​

Lateral Surface Area

​S, Total = 2π​r² + 2πrh

S = 2π​r² + 2πrh​

​S = 2(3.14)(3)² + 169.56

S = 226. 08 in²​

Use 3.14 for π

​

R = Radius = 3

H = Height = 9

L = 169.56 in²​

​

Multiple Choice

An ice cream cone and its dimensions are shown below. Find the volume of the ice cream cone in cubic centimeters?

 

• 113 cm²

• 28 cm²

• 452 cm²

• 114 cm²

Multiple Choice

Going from least to greatest, what is the volume of each shape?

• 2.09 cm² ,6.28 cm², 4.19 cm²

• 6.28 cm², 4.19 cm², 2.09 cm²

• 2.09 cm², 4.19 cm², 6.28 cm²,

• 6.28 cm², 2.09 cm² ,4.19 cm²

Multiple Choice

A container is shaped like a triangular prism. Each base of the container is an equilateral triangle with the dimensions shown. The container has a height of 10 centimeters. What is the lateral surface area of the container in square centimeters?

• 120 cm²

• 80 cm²

• 160 cm²

• none of the above

Multiple Select

The dimensions of some cylinders are given below. Which of the following cylinders have the same volume? Select 2 answer choices.

• Radius - 2

  height - 4

• Radius - 1

  height - 8

• Radius - 4

  height - 2

• Radius - 4

  height - 1

• Radius - 1

  height - 4

Multiple Choice

A cylinder has a diameter of 6 yards and a height of 7 yards. Which expression can be used to find V, the volume of the cylinder in cubic feet?

• π(6)(7)

• π(6)²(7)

• π(6)(7)²

• π(3)²(7)

Multiple Choice

A ball, shaped like a sphere, has a diameter of 6 centimeters. What is the volume of the ball in cubic centimeters?

(Use 3.14 for )

• 226.08 cm³

• 37.68 cm³

• 113.04 cm³

• 28.26 cm³

Multiple Choice

A cylinder shaped pipe is 15 inches long and has a diameter of 10 inches. What is the lateral surface area of the pipe in square inches?

• 471 in²

• 235.5 in²

• 628 in²

• 942 in²

Multiple Choice

A triangular prism and its dimensions are shown in the diagram. The height of the triangle is 4 cm.What is the total surface area of this triangular prism in square centimeters?

• 140 cm²

• 150 cm²

• 152 cm²

• 158 cm²

Multiple Choice

Jason wants to paint his storage shed. He needs to calculate the lateral surface area of the shed so that he will know how much paint to buy. The shed is in the shape of a rectangular prism with the dimensions shown below.Including the doors, what is the lateral surface area of the storage shed in square feet?

• 648 ft²

• 162 ft²

• 234 ft²

• 324 ft²

Fill in the Blank

What is the total surface area of the rectangular prism shown in the figure? Round the nearest whole number.

Fill in the Blank

A rancher needs a cylinder-shaped water tank 10 meters across and 29 meters high to store water for the summer months. Find how much material he will need to construct the tank? (Use 3.14 for ) Round to the tenth place.