3D Shapes and Volume Calculations

The video tutorial covers drawing 3D solids by rotating 2D shapes, identifying 3D solids from nets, naming cross-sections, calculating volumes, and understanding volume changes with scale factors. It provides step-by-step instructions and examples to help students visualize and compute geometric properties.

What shape is formed when a rectangle is rotated around one of its sides?

• Sphere

• Cylinder

• Cone

• Cube

Which 3D shape is formed by folding a net with two triangular bases and three rectangular sides?

• Cylinder

• Cone

• Rectangular Prism

• Triangular Prism

What is the horizontal cross-section of a cone?

• Circle

• Triangle

• Square

• Rectangle

How do you calculate the volume of a pyramid?

• Base area × height × 3

• Base area × height / 2

• Base area × height / 3

• Base area × height

Which solid has a volume of 40 cubic units if its base area is 20 and height is 2?

• Sphere

• Rectangular Prism

• Cylinder

• Cone

If a cylinder has a height of 4 cm and a volume of 144π cubic cm, what is its radius?

• 4 cm

• 8 cm

• 6 cm

• 3 cm

What happens to the surface area when a shape is dilated by a scale factor of 4?

• Multiplies by 64

• Multiplies by 8

• Multiplies by 16

• Multiplies by 4

How do you find the scale factor if the volume of a dilated shape is 21.4 and the original is 8.6?

• Divide the volumes

• Cube root the volume ratio

• Square the volume ratio

• Multiply the volumes

If a rectangle with an area of 24 in² is dilated by a scale factor of 3, what is the new area?

• 144 in²

• 72 in²

• 48 in²

• 216 in²