Two- and Three-Dimensional Shapes

What cross section is made when a plane slices perpendicular to the base of a square pyramid?

• Square

• Triangle

• Trapezoid

• Circle

Answer explanation

When a plane slices perpendicular to the base of a square pyramid, it creates a triangle cross section. This is because the intersection of the plane with the pyramid forms a triangle shape.

What cross section is made when a plane slices perpendicular to the base of a cylinder.

• Circle

• Triangle

• Rectangle

• Ellipse

Answer explanation

A plane slicing perpendicular to the base of a cylinder creates a rectangle cross-section, as the base of a cylinder is a circle and the intersection forms a rectangle.

What cross section is made when a plane slices parallel to the base of this triangular prism?

• Rectangle

• Circle

• Triangle

• Square

Answer explanation

When a plane slices parallel to the base of a triangular prism, the cross section formed is a triangle, as it will have the same shape as the base of the prism.

Select the 2D object that can be rotated to form the 3D object shown.

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What cross section is made when a plane slices parallel to the base of a cone.

• Dome

• Circle

• Pyramid

• Triangle

Answer explanation

When a plane slices parallel to the base of a cone, the cross section formed is a circle. This is because the intersection of the plane with the cone results in a circular shape.

A stack of 6 square blocks is shown, where the side length of each square block is 5.75 inches and has a thickness of 0.12 inches.

What is the square area of the stack of square blocks?

• 33.07 sq. in

• 31.08 sq. in

• 34.93 sq. in

• 32 sq. in

Answer explanation

The square area of the stack of square blocks can be calculated by multiplying the side length of each block by the total number of blocks in the stack. Therefore, 5.75^2 * 6 = 33.07 sq. in.

Find the volume of the following object.  Use the reference sheet for the formula.

A sphere with the diameter of 4.4 ft.

Answer explanation

The volume of a sphere is calculated using the formula V = (4/3)πr^3. Given the diameter is 4.4 ft, the radius is half of that, which is 2.2 ft. Plugging in the values, V = (4/3)π(2.2)^3 = 14.2π ft^3.

Find the volume of the following shape:

Rectangular prism with the dimensions of:

Height 3 cm

Length 8 cm

Width 5 cm

• 120 cubic cm

• 16 cubic cm

• 40 cubic cm

• 21 cubic cm

Answer explanation

To find the volume of a rectangular prism, multiply the height, length, and width: 3 cm * 8 cm * 5 cm = 120 cubic cm. Therefore, the correct answer is 120 cubic cm.

Find the volume for the following shape. 

Use you reference sheet for the formula.

Rectangular pyramid  

Height 4 cm

Length  8 cm

width  3 cm

Answer explanation

The volume of a rectangular pyramid is calculated using the formula V = (1/3) * base area * height. In this case, base area = length * width = 8 * 3 = 24 cm^2. Substituting in the values, V = (1/3) * 24 * 4 = 32 cm^3, so the correct answer is 32 cm^3.

Find the volume for the following shape. 

Use you reference sheet for the formula.

A cone with a diameter of 20 inches and a height of 12 inches.

• 1256.64 cubic inches

• 240 cubic inches

• 5026.55 cubic inches

• 1507.96 cubic inches

Answer explanation

The correct volume for a cone is calculated using the formula V = (1/3) * π * r^2 * h. Given the diameter is 20 inches, the radius is 10 inches. Plugging in the values, V = (1/3) * π * 10^2 * 12 = 1256.64 cubic inches.