Surface Area of Pyramids and Cones

Surface Area of Pyramids and Cones

By Deb Scott

​Let's look at the names of the parts of a pyramid. Pyramids are named by the shape of their base.

Multiple Choice

What does the "l" mean in the formula?

• perimeter of the base

• slant height

• Height

• I was not paying attention

Multiple Choice

What is the formula for LA?

• $$\frac{1}{2}$$  pl

• pl

• LA + B

Multiple Choice

Find the surface area of the square pyramid.

• 15 square meters
• 39 square meters
• 69 square meters
• 30 square meters

Multiple Choice

What is the surface are if you were to wrap this square pyramid?

• 23 sq. meters
• 27 sq. meters
• 33 sq. meters
• 36 sq. meters

Multiple Choice

Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.

• 152.6 cm²; 187.7 cm²
• 212 ft²; 322 ft²
• 219.6 in²; 313.2 in²
• 50.4 in²; 66.4 in²

Multiple Choice

Find the surface area of the figure.

Round your answer to the nearest hundredth. (Hint: you'll have to use Pythagorean Theorem to find the slant height)

• 2,400 $$ft^2$$

• 1,200 $$ft^2$$

• 1,560 $$ft^2$$

• 18,000 $$ft^2$$

Multiple Choice

How do you find the lateral area of a pyramid?

• $$\pi rl$$  

• $$\pi rl+\pi r^2$$  

• $$\frac{1}{2}Pl$$

• $$\frac{1}{2}Pl+B$$

Multiple Choice

How do you find the total surface area of a pyramid?

• $$\pi rl$$  

• $$\pi rl+\pi r^2$$  

• $$\frac{1}{2}Pl$$

• $$\frac{1}{2}Pl+B$$

​Now let's look at the vocabulary of a cone

Multiple Choice

How do you find the lateral area of a cone?

• $$\pi rl$$  

• $$\pi rl+\pi r^2$$  

• $$\frac{1}{2}Pl$$

• $$\frac{1}{2}Pl+B$$

Multiple Choice

How do you find the total surface area of a cone?

• $$\pi rl$$  

• $$\pi rl+\pi r^2$$  

• $$\frac{1}{2}Pl$$

• $$\frac{1}{2}Pl+B$$

Multiple Choice

Both the pyramid and cone have a what?

• Slant height

• Circular base

• Triangular base

• Rectangular face

Multiple Choice

Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.

• 203.4 m²; 297 m²
• 37.7 m²; 50.3 m²
• 50 m²; 75 m²
• 150 m²; 254.5 m²

Multiple Choice

Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.

• 183.0 cm²; 233.2 cm²
• 188 cm²; 259 cm²
• 83.7 cm²; 93.2 cm²
• 190 cm²; 240 cm²

Multiple Choice

What is the total surface area of the cone?

• 91.374 in²

• 56.52 in²

• 169.56 in²

• 28.3 in²

Multiple Choice

What is the lateral area?

• 449.88 mi²

• 1704 mi²

• 650.94 mi²

• 899.75 mi²

Multiple Choice

A paper party hat, like the one shown, has a slant height of 6 inches and a height of 5 inches. How many square feet of cardboard would be needed to create this hat?

• 62.5 in.²
• 10 in.²
• 50 in.²
• 22.5 in.²

Multiple Choice

Find the surface area

• 1276.3m²

• 824.7m²

• 1649.3m²

• 3534.3m²

Fill in the Blanks

Find the surface area of the pyramid. No units needed in your answer.

Multiple Choice

What is the SURFACE AREA of this pyramid?    SA=

• $$117\ m^2$$

• $$729\ m^2$$

• $$243\ m^2$$

• $$81\ m^2$$

Multiple Choice

This formula is to find the surface area of which solid?

• Cone

• Sphere

• Cylinder

• Circumference

Multiple Choice

What is the lateral area of the pyramid?

• 384 cm²

• 256 cm²

• 640 cm²

• 28 cm²

Multiple Choice

Find the surface area.

• 728.5 cm sq
• 1007.9 cm sq
• 1513.5 cm sq
• 1462 cm sq

Multiple Choice

What does lateral mean when asked to find the lateral surface area?

• Means the bases and no sides.
• Means just  the sides.
• Means everything.

Multiple Choice

A pyramid has a square base. Each side of the base is 9 cm. The slant height of each triangle is 14 cm. What is the surface area?

• 126 cm²
• 144 cm²
• 252 cm²
• 333 cm²