Volume and Surface Area Concepts

The video tutorial covers the calculation of volumes for composite solids, which are combinations of basic shapes like cylinders, prisms, and spheres. It begins with an introduction to composite solids and proceeds with a detailed example involving a rectangular prism and a half-cylinder. The tutorial then provides a practice problem with a rectangular prism and a full cylinder, followed by an advanced problem featuring a cylinder with a cylindrical hole. Throughout the video, the instructor emphasizes using the approximation 3.14 for pi and rounding to the nearest tenth.

What is the first step in solving problems involving composite solids?

• Calculate the total surface area

• Name the individual shapes

• Find the perimeter of the base

• Determine the weight of the solid

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

When calculating the volume of a half-cylinder, what operation is typically used?

• Division

• Multiplication

• Subtraction

• Addition

Tags

CCSS.7.G.B.6

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

• Base times Height divided by 2

• 4/3 pi r cubed

• Length times Width times Height

• pi r squared h

Tags

CCSS.7.G.B.4

How do you determine the radius if only the diameter is given?

• Multiply the diameter by 2

• Divide the diameter by 2

• Subtract 2 from the diameter

• Square the diameter

Tags

CCSS.5.MD.C.5C

What is the next step after calculating the individual volumes of shapes in a composite solid?

• Divide the volumes

• Multiply the volumes

• Add the volumes together

• Subtract the smaller volume from the larger one

Tags

CCSS.5.MD.C.5C

In the problem involving a rectangular prism and a full cylinder, what is the final step?

• Multiply the volumes of the prism and cylinder

• Add the volumes of the prism and cylinder

• Subtract the volume of the cylinder from the prism

• Divide the volume of the prism by the cylinder

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• pi r squared h

• Length times Width times Height

• 4/3 pi r cubed

• Base times Height divided by 2

Tags

CCSS.5.MD.C.5C

How do you handle a problem involving a cylinder with a cylindrical hole?

• Divide the volume of the large cylinder by the small cylinder

• Subtract the volume of the small cylinder from the large cylinder

• Add the volumes of the large and small cylinders

• Multiply the volumes of the large and small cylinders

Tags

CCSS.HSG.GMD.A.1

What is the purpose of using the approximation 3.14 for pi in these problems?

• To avoid using a calculator

• To make calculations easier

• To increase the accuracy

• To reduce the number of steps

Tags

CCSS.HSG.GMD.A.1

What should you do if you get a problem wrong in this video tutorial?

• Skip to the next problem

• Rewatch the video and find your mistake

• Ask a friend for help

• Ignore the mistake and move on