Final Topic: 3D Figures

Open Ended

What is the difference between the two sets of figures on the previous slide?

Multiple Choice

What is the main difference between surface area and volume for a 3D figure?

• Surface area measures the total area of all surfaces, while volume measures the space occupied.

• Surface area measures the space inside, while volume measures the outside.

• Surface area is always larger than volume.

• Volume is measured in square units, while surface area is in cubic units.

Multiple Choice

Which formula represents the surface area of a sphere?

• A = 4πr²

• A = 2πrh + 2πr²

• A = πr²h

• A = 6a²

Multiple Select

Select all the correct statements about a cylinder.

• A cylinder has two circular faces.

• A cylinder has edges and vertices.

• A cylinder's surface area is given by 2πrh + 2πr².

• A cylinder's volume is given by πr²h.

Multiple Choice

What is the formula for the volume of a cylinder?

• V = πr²h

• V = 2πrh

• V = πd²h

• V = 2πr²

Fill in the Blanks

A cylindrical water tank has a diameter of 2 meters and a height of 4 meters. The tank is filled with water to a height of 3 meters. How much water (in liters) is in the tank?

Multiple Choice

How many liters of water can a cylinder with a radius of 1 meter and a height of 3 meters hold?

• 9420 L

• 3000 L

• 4710 L

• 3140 L

Open Ended

Describe how the properties of a sphere differ from those of a cylinder.

Fill in the Blanks

A pyramid has one

and at least three triangular sides.

Multiple Choice

Which formula would you use to calculate the volume of a pyramid?

• V = lwh/3

• V = πr^2h/3

• V = lwh

• V = 2(wl + hl + hw)

Open Ended

Explain how you would find the volume of a pyramid if you know the area of its base and its height.

Multiple Choice

Which of the following statements about a cone is correct?

• A cone has one round face and no edges or vertices.

• A cone has two round faces and one edge.

• A cone has one round face and one vertex.

• A cone has two round faces and no vertices.

Open Ended

Compare the surface area formulas for a pyramid and a cone. What similarities and differences do you notice?

Multiple Select

Select all the properties that correctly describe a prism.

• Has two congruent parallel bases

• Has only one round face

• Has some number of sides

• Has no edges or vertices

Fill in the Blanks

Fill in the blank: The formula for the surface area of a prism is A =

(wl + hl + hw).

Multiple Choice

Given a rectangular prism with dimensions 25 cm by 10 cm by 5 cm and a sphere with a radius of 4 in, which formulas would you use to calculate their surface areas?

• 2lw + 2lh + 2wh for the prism, 4πr^2 for the sphere

• πr^2h for both shapes

• lwh for the prism, 2πr^2 for the sphere

• 4πr^2 for the prism, 2lw + 2lh + 2wh for the sphere

Open Ended

Jiah is gifting his best friend a box of donuts. He wants to wrap it so he can keep the gift a surprise. If the box is 22cm x 15cm x 5cm, what is the minimum amount of wrapping paper he needs?

Fill in the Blanks

The volume of a cube is represented by the formula V =

³.

Multiple Choice

Given the surface area of a cube is 338 cm², what is the length of one side of the cube?

• 6.5 cm

• 13 cm

• 8 cm

• 5.8 cm

Fill in the Blanks

What is the volume of a cube with a surface area of 338 square centimeters?

Open Ended

Classify each solid figure and calculate the surface area of each figure shown in the previous slide.

Multiple Choice

Which of the following figures has a greater volume: a pyramid with a base of 8 cm by 8 cm and a height of 12 cm, or a cylinder with a radius of 4 in and a height of 9 in?

• The pyramid has a greater volume.

• The cylinder has a greater volume.

• Both have the same volume.

• Cannot be determined from the information given.

Multiple Choice

Which of the following best describes the difference between surface area and volume for 3D figures?

• Surface area is the amount of space inside a figure, while volume is the area covering the outside.

• Surface area is the total area of all the surfaces of a 3D figure, while volume is the amount of space occupied by the figure.

• Surface area and volume are always equal for any 3D figure.

• Surface area is only used for 2D shapes, while volume is for 3D shapes.

Open Ended

Explain why different 3D figures require different formulas for calculating surface area and volume. Provide examples using at least two different figures.