Volume and Surface Area Formulas

This video tutorial covers the calculation of volume for various geometric shapes, including cylinders, spheres, cones, rectangular prisms, and cubes. It provides step-by-step instructions and formulas for each shape, using specific examples to illustrate the process. The tutorial also explains how to convert results into decimal form and discusses the impact of using different values of pi on the final answer.

What is the formula for calculating the volume of a cylinder?

• V = lwh

• V = πr²h

• V = 4/3πr³

• V = 1/3πr²h

If a cylinder has a radius of 4 inches and a height of 6 inches, what is its volume in terms of π?

• 24π cubic inches

• 96π cubic inches

• 48π cubic inches

• 192π cubic inches

Given the surface area of a sphere is 256π square feet, what is the formula to find its volume?

• V = lwh

• V = 1/3πr²h

• V = πr²h

• V = 4/3πr³

What is the radius of a sphere if its surface area is 256π square feet?

• 10 feet

• 8 feet

• 16 feet

• 4 feet

How do you calculate the volume of a cone?

• V = lwh

• V = 4/3πr³

• V = πr²h

• V = 1/3πr²h

What is the volume of a cone with a radius of 5 cm and a height of 8 cm in terms of π?

• 200π/3 cubic cm

• 250π/3 cubic cm

• 100π/3 cubic cm

• 150π/3 cubic cm

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

• V = 4/3πr³

• V = 1/3πr²h

• V = πr²h

• V = lwh

Calculate the volume of a rectangular prism with dimensions 4 feet by 5 feet by 6 feet.

• 160 cubic feet

• 100 cubic feet

• 120 cubic feet

• 140 cubic feet

How do you find the side length of a cube if you know the length of its diagonal?

• Multiply the diagonal by 3

• Divide the diagonal by 3

• Multiply the diagonal by the square root of 3

• Divide the diagonal by the square root of 3

What is the volume of a cube with a side length of 7 cm?

• 343 cubic cm

• 21 cubic cm

• 196 cubic cm

• 49 cubic cm