Surface Area of Prisms and Cylinders

Surface Area of Prisms and Cylinders

By Deb Scott

​Objective: Find the Surface Area of Prisms and Cylinders

What is a prism?

A Prism is a solid object with a uniform cross-section and all sides flat.

In oblique prisms, some of the lateral faces are nonrectangular.​

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​Oblique Prisms

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In right prisms, the lateral faces are rectangles and a lateral edge is an altitude​

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​Right Prisms

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​We will only be using right prisms

for this lesson

Surface Area vs. Lateral Area

• Surface Area is the area of all the sides of the 3D figure, including the bases.

• Lateral Area DOES NOT include the bases.

Area abbreviations

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• P = Perimeter of the Base

• B = Area of the Base

• h = height between the bases

• r = radius of a circular base

• L.A. = Lateral Area

• S.A. = Surface Area​

Multiple Choice

What does "P" stand for in the surface area formulas?

• Perimeter
• Parallel
• Perimeter of the Base
• Pi

Multiple Choice

What does "B" stand for in the surface area formulas?

• Bottom of the Prism

• Perimeter of the Base
• Area of the Base

Lateral and Surface Area of a Prism

Lateral Area of a right prism is the product of the perimeter of the base and the height of the prism.

L.A. = ph

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Surface area of a right prism is the sum of the lateral area and the areas of the​ two bases.

S.A. = L.A. + 2B​

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Multiple Choice

Jesse needs to wrap the present shown below. How much wrapping paper would he need? Is this asking for Lateral or Surface area?

• Lateral Area

• Surface Area

Multiple Choice

What is lateral area?

• Inside of the object
• The sum of all the areas of all the shapes that cover the surface of the object.
• The sum of all the lateral faces of the object.

Multiple Choice

Jesse needs to wrap the present shown below. How much wrapping paper would he need?

Which formula can be used to find the surface area of the present?

• SA=Ph+2B
• SA=2πrh+2πr²
• SA=Ph
• V=Bh

Multiple Choice

Jesse needs to wrap the present shown below. How much wrapping paper would he need?
How much wrapping paper is needed?

• 300 in²
• 558 in²
• 327 in²
• 354 in²

Lateral Area and Surface Area of a Cylinder​

L.A. = 2​πrh or L.A. = πdh

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S.A. = L.A. + 2B or S.A. = 2πrh + 2πr²

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Multiple Choice

What is the surface area formula for a cylinder?

• SA = πrl + πr²
• SA = 2πrh + 2πr²
• SA = 4πr²
• SA = πr²h

Multiple Choice

Find the total surface area of the cylinder.

• 100.53 square inches
• 351.86 square inches
• 251.33 square inches
• 50.27 square inches

Fill in the Blank

Find: LA Use 3.14 for pi and round to the nearest tenth

Fill in the Blank

Find: SA

Multiple Choice

Find the Surface Area

• 556 cm²

• 278 cm²

• 680 cm²

• 340 cm²

Multiple Choice

_{Find the Surface Area}

• 500 ft²

• 515 ft²

• 525 ft²

• 510 ft²

Multiple Choice

Find the total surface area of the prism.

• 161 square feet
• 1,700 square feet
• 75 square feet
• 186 square feet

Fill in the Blank

Find L.A.

Fill in the Blank

Find S.A.

Multiple Choice

Campbell Soup is creating a new soup label. If a can has a height of 6 in and a diameter of 4 in, how much material does Campbell need for each soup label? Use 3.14 for π.

What is the surface area of the label?

• 150.72 in²
• 100.48 in²
• 24 in²
• 75.36 in²

Multiple Choice

A wax coating is used to cover a wheel of cheese in order to keep it fresh.  If the cheese wheel has a diameter of 8 in and a height of 5 in, calculate the total surface area needed to cover the entire wheel of cheese. 

• 40 in²
• 125.7 in²
• 175.9 in²
• 226.2 in²

Multiple Choice

A cylinder has a diameter of 6 mm and a height of 18 mm.  Find its lateral surface area.

• 339.29 mm²
• 62.83 mm²
• 395.84 mm²
• 169.65 mm²

Multiple Choice

What shape is this?

• Cylinder
• Rectangular Prism
• Cube
• Cone

Multiple Choice

What shape is this?

• Cylinder
• Rectangular Prism
• Cube
• Cone