Geometric Volume and Surface Area

This video tutorial covers common 3D shapes including spheres, cylinders, cones, rectangular prisms, and cubes. It explains the formulas for calculating the volume and surface area of each shape, providing examples and detailed explanations. The video also discusses the concept of slant height for cones and the diagonal length for rectangular prisms and cubes.

What is the formula for the volume of a sphere?

• 4/3 πr³

• 2πr²

• πr²h

• 1/3πr²h

If the radius of a sphere is 5 cm, what is its surface area using π as 3.14?

• 157 cm²

• 314 cm²

• 100 cm²

• 78.5 cm²

How do you calculate the volume of a cylinder?

• 4/3πr³

• 2πrh

• 1/3πr²h

• πr²h

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

• 2πr² + 2πrh

• πr² + πrl

• 4πr²

• 2πr²h

What is the volume of a cone in relation to a cylinder with the same base and height?

• One-third of the cylinder's volume

• Equal to the cylinder's volume

• Twice the cylinder's volume

• Half of the cylinder's volume

How do you find the slant height of a cone?

• Using the formula 2πr

• Using the Pythagorean theorem

• By measuring the base

• By doubling the radius

What is the formula for the volume of a rectangular prism?

• 4/3πr³

• πr²h

• 2lw + 2wh + 2lh

• Length × Width × Height

How can you calculate the diagonal length of a rectangular prism?

• √(w² + h² + l²)

• w + h + l

• πr² + πrl

• 2(lw + wh + lh)

What is the formula for the volume of a cube?

• Side³

• Length × Width × Height

• πr²h

• 4/3πr³

How do you calculate the diagonal length of a cube?

• 3 × Side

• √3 × Side

• Side × Side

• 2 × Side