Geometry of 3D Shapes

This video tutorial covers various geometric concepts related to three-dimensional shapes, including prisms, limas, cubes, and baloks. It explains how to calculate diagonals, surface areas, and the number of sides and edges for these shapes. The video provides step-by-step solutions to example problems, helping students understand the application of formulas in geometry.

What are the main topics covered in this video tutorial?

• Geometry of 3D shapes

• Statistics and Probability

• Algebra and Calculus

• Trigonometry and Functions

Which line connects two opposite corners in a 3D shape?

• Vertex

• Diagonal of the space

• Diagonal of a face

• Edge

How do you calculate the number of faces in a prism with a polygonal base?

• n + 2

• 2n

• 3n

• n + 1

What is the formula for the diagonal of a cube's face?

• a√2

• a√3

• 2a

• 3a

If the diagonal of a cube's face is 6√2 cm, what is the side length of the cube?

• 3 cm

• 12 cm

• 9 cm

• 6 cm

What is the total surface area of a cube with a side length of 5 cm?

• 25 cm²

• 50 cm²

• 150 cm²

• 125 cm²

How many edges does a cuboid have?

• 10

• 6

• 12

• 8

What is the formula for the surface area of a prism?

• Base area + perimeter

• Base area × height

• 2 × base area + perimeter × height

• Perimeter × height

If a prism has a square base with an area of 36 cm² and a height of 20 cm, what is its total surface area?

• 180 cm²

• 360 cm²

• 72 cm²

• 252 cm²

What is the length of the side of a square base if the perimeter is 40 cm?

• 20 cm

• 5 cm

• 10 cm

• 15 cm