Volume of Square Pyramids and Cones Lesson

​Volume of Square Based Pyramids & Cones

SOL 8.6a    

The student will solve problems, including practical problems, involving the volume and surface area of cones and square-based pyramids.

​Dessert?

or Desert?

Square Pyramid Inquiry

Multiple Choice

What is the volume of the cube if one side measures 6 feet?

Hint:

$$V=lwh$$

• 18 ft³

• 6 ft³

• 216 ft³

• 36 ft³

Multiple Choice

The height of this square pyramid is 6 feet and the length of one of its sides is 6 feet use the formula below to find the pyramid's volume. $$V=\frac{1}{3}Bh\ where\ B\ is\ lw$$

• $$72ft^3$$

• $$216ft^3$$

• $$6ft^3$$

• $$12ft^3$$

​Given the information that one side length was 6 feet you found the volume by calculating 6 x 6 x 6 = 216.

​​The volume of the cube in slide 3 was 216 cubic feet.

Given the information that one side length was 6 feet you found the volume by calculating

1/3 (6 x 6 x 6) = 72. Now try (6 x 6 x 6) ÷ 3.

Did you get 72?

The volume of the square pyramid in slide 4 was 72 cubic feet.

​Understanding the Formula

Square pyramids are 1/3 of cubes with the same side lengths. This means you are simply finding:

length x width x height then divide by 3

Easy peezy, lemon squeezy!

Cone Inquiry

Multiple Choice

What is the volume of the cylinder in the image?

Round to the nearest whole number.

Use the formula:

$$V=\pi r^2h$$

• 123 m³

• 503 m³

• 1257 m³

• 126 m³

Multiple Choice

The height of this cone is 10 meters and the radius is 4 meters use the formula below to find the cone's volume. $$V=\frac{1}{3}\pi r^2h$$

Round to the nearest whole number.

• $$105m^3$$

• $$419m^3$$

• $$42m^3$$

• $$168m^3$$

​Given the information that the

height is 10 meters and the radius is 4 meters you multiplied 4² x 10 x 3.14 to find a volume of ≈ 503 cubic meters.

​​The volume of the cylinder in slide 8 was 503 cubic meters.

Given the information that the cone's

height is 10 meters and the radius is 4 meters you multiplied 1/3 x 4² x 10 x 3.14 to find a volume of ≈ 168 cubic meters. Now try 4² x 10 x 3.14 and divide by 3. Did you get 168?

The volume of the cone in slide 9 was 168 cubic meters.

​Understanding the Formula

Cones are 1/3 of cylinders with the same height and radius. This means you are simply finding:

(radius)² x height x 3.14 then divide by 3

Easy peezy, lemon squeezy!

Practice Time!

Multiple Choice

Find the volume of the figure.

• 1,800 cm³

• 900 cm³

• 600 cm³

• 750 cm³

Multiple Choice

Find the volume of this figure.

• 190cm³

• 200cm³

• 140cm³

• 192cm³

Multiple Choice

The pyramid caste used to make this chocolate pyramid has a depth of 4 inches and a width of 4 inches. What is the volume of chocolate used in the caste?

Round to the nearest whole number.

• 21 in³

• 64 in³

• 32 in³

• 11 in³

Multiple Choice

Find the volume of the figure.

• 150.72 cm³

• 75.36 cm³

• 452.16 cm³

• 151 cm³

Multiple Choice

Find the volume to the nearest hundredth.

• 12.56 ft³

• 37.68 ft³

• 18.84 ft³

• 6.28 ft³

Multiple Choice

Find the volume. Round to the nearest tenth.

Hint: Radius is half of the diameter.

• 718.4 km³

• 2155.1 km³

• 196 km³

• 205.3 km³

Multiple Choice

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

• 21 cubic inches

• 63 cubic inches

• 66 cubic inches

• 198 cubic inches