Finding Volume through Decomposition Techniques

The video tutorial explains how to calculate the volume of a complex figure by dividing it into two rectangular prisms. The instructor provides the dimensions and demonstrates the calculation process for each prism separately. The blue prism has dimensions of 3 cm by 5 cm by 7 cm, resulting in a volume of 105 cubic centimeters. The magenta prism has dimensions of 9 cm by 2 cm by 7 cm, resulting in a volume of 126 cubic centimeters. The total volume of the figure is calculated by summing the volumes of the two prisms, resulting in a total volume of 231 cubic centimeters.

What is the first step in calculating the volume of the given figure?

• Identify the figure as a single complex shape.

• Break the figure into two rectangular prisms.

• Calculate the volume using the formula for a sphere.

• Ignore the dimensions and estimate visually.

Which method is used to simplify the volume calculation?

• Combining into a single complex shape

• Using a water displacement method

• Breaking it down into cylindrical shapes

• Dividing it into rectangular prisms

What are the dimensions of the first rectangular prism?

• Width: 7cm, Height: 5cm, Length: 3cm

• Width: 5cm, Height: 3cm, Length: 7cm

• Width: 2cm, Height: 7cm, Length: 12cm

• Width: 3cm, Height: 5cm, Length: 7cm

How is the volume of a rectangular prism calculated?

• Length x Width x Height

• Length + Width + Height

• (Length + Width) x Height

• Length / Width / Height

What is the volume of the first rectangular prism?

• 125 cubic centimeters

• 95 cubic centimeters

• 105 cubic centimeters

• 115 cubic centimeters

How do you find the missing dimension of the second prism?

• Subtract the length of the first prism from the total length.

• Add the lengths of both prisms together.

• Subtract the width of the first prism from the total length.

• Subtract the width of the first prism from the total width.

What is the depth of the second rectangular prism?

• 12 centimeters

• 5 centimeters

• 7 centimeters

• 9 centimeters

What is the volume of the second rectangular prism?

• 126 cubic centimeters

• 146 cubic centimeters

• 136 cubic centimeters

• 116 cubic centimeters

Which dimensions are used to calculate the volume of the magenta part?

• 9cm x 7cm x 2cm

• 12cm x 3cm x 2cm

• 7cm x 5cm x 3cm

• 5cm x 7cm x 9cm

What is the total volume of the figure?

• 211 cubic centimeters

• 231 cubic centimeters

• 221 cubic centimeters

• 241 cubic centimeters