Volume and Area of Solids

This video tutorial covers the calculation of volumes for various 3D shapes, including prisms, cylinders, pyramids, cones, and spheres. It explains the formulas used for each shape and provides example calculations. The tutorial also discusses composite shapes and offers information on an online exam for further practice.

What is the formula to find the area of the cross-section of a triangular prism?

• Base times height

• Base plus height

• Base minus height

• Half times base times height

How do you calculate the volume of a prism once you have the area of the cross-section?

• Multiply by the base

• Multiply by the height

• Multiply by the length

• Multiply by the width

What is the formula for the area of the circular base of a cylinder?

• 2πr

• 2πr²

• πr²

• πd

To find the volume of a cylinder, you multiply the area of the base by which dimension?

• Diameter

• Height

• Radius

• Width

What is the shared formula for calculating the volume of both pyramids and cones?

• 2/3 base area times height

• 1/3 base area times height

• Base area times height

• 1/2 base area times height

In a square-based pyramid, if one side of the base is 14 mm, what is the area of the base?

• 196 mm²

• 28 mm²

• 14 mm²

• 392 mm²

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

• πr³

• 2/3 πr³

• 4/3 πr³

• 4/3 πr²

If the radius of a sphere is 3, what is the volume in terms of π?

• 27π

• 54π

• 18π

• 36π

In the composite shape example, what is the first step to find the total volume?

• Add the volumes of the cone and cylinder

• Subtract the volume of the cone from the cylinder

• Multiply the volumes of the cone and cylinder

• Divide the volume of the cylinder by the cone

What is the total volume of the composite shape consisting of a cone on top of a cylinder, rounded to one decimal place?

• 300.5 mm³

• 200.0 mm³

• 150.7 mm³

• 242.9 mm³