Exploring Volumes of 3-D Solids Worksheet

Total Time: 65 minutes

Introduction to 3-D Solids Volume

Time: 5 minutes

Let's review what we know about the basic 3-D shapes. Write down the formulas for the volumes of the following solids:

Prism
Pyramid
Cone
Sphere
Cylinder

Use your textbook or class notes if needed!

Volume and Dimensions Discovery

Time: 15 minutes

Complete the following problems. Remember to show your work:

A rectangular prism has a length of 10 cm, a width of 5 cm, and an unknown height. If its volume is 250 cm³, what is the height?
The volume of a cone is 80 cm³. If the radius is 4 cm, calculate the height of the cone.
A pyramid has a square base with a side length of 6 cm and a height of 9 cm. Calculate its volume.

Composite Shapes Challenge

Time: 15 minutes

Consider the composite shape made up of a cylinder and a hemisphere stuck together. The cylinder has a height of 10 cm and a radius of 3 cm, while the hemisphere has the same radius.

Calculate the total volume of the composite shape.
If the height of the cylinder were unknown but you know the total volume is 100 cm³, how would you find the height?

Real-World Volume Application Word Problems

Time: 10 minutes

Read the following scenarios and answer the questions:

A water tank in the shape of a cylinder has a radius of 1.5 m and a height of 2 m. If it is filled to 3/4 of its height, how much water is in the tank?
A soccer ball is a sphere with a diameter of 22 cm. What is the volume of the soccer ball? How much space does it occupy?

Creative Project: Volume in Action

Time: 20 minutes

Working in pairs, create a visual representation of your favorite 3-D solid. Include:

Formula for volume
A word problem related to that solid
An infographic illustrating how to solve the volume of your solid Present your diagram to the class!