Inside Maths: Volume of 3-Dimensional Shapes

The video tutorial explores the concepts of prisms and cylinders, focusing on their constant cross-sections. It demonstrates how to calculate the volume of these shapes using practical examples, such as cakes and fish tanks. The tutorial also covers advanced volume calculations for complex shapes and guides viewers in designing a custom cylindrical fish tank, ensuring it meets specific volume requirements.

What defines a prism in terms of its cross-section?

• It has a circular cross-section.

• It has a constant cross-section throughout its length.

• It has a triangular cross-section.

• It has a variable cross-section.

Why is a Battenburg cake considered a prism?

• Because it is made of layers.

• Because it has a variable cross-section.

• Because it has a constant cross-section with straight edges.

• Because it has a circular cross-section.

How do you calculate the volume of a prism?

• Multiply the area of the cross-section by the height.

• Add the area of the cross-section to the height.

• Subtract the height from the area of the cross-section.

• Divide the area of the cross-section by the height.

What is the first step in determining the volume of a fish tank?

• Weigh the tank.

• Fill the tank with water.

• Measure the height of the tank.

• Calculate the cross-sectional area.

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

• Length x Width x Height

• Length - Width - Height

• Length + Width + Height

• Length / Width / Height

How do you convert cubic centimeters to liters?

• Multiply by 1000

• Divide by 1000

• Add 1000

• Subtract 1000

What shape is the cross-section of the custom fish tank?

• Rectangle

• Square

• Triangle

• Circle

What is the minimum height required for the custom cylindrical tank to hold 35 liters?

• 20 cm

• 43.5 cm

• 60 cm

• 80 cm

What is the formula for the area of a circle?

• 2πr

• 2πd

• πd

• πr^2

Why was the volume calculation for the body-shaped fish tank incorrect?

• The wrong height was used.

• The tank was not filled with water.

• The cross-section was taken from the wrong part of the tank.

• The formula for volume was incorrect.