MA19.7A.40

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.40
Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions. [Grade 8, 29]

Unpacked Content

Knowledge

Students know:

The difference between volume and surface area.
That volume is defined as the number of unit cubes needed to create or fill the 3-dimensional figure

Skills

Students are able to:

find the volume of cones, cylinders, and spheres
Show the relationship between the volume of a cone, a cylinder, and a sphere with the same radius.

Understanding

Students understand that:

volume can be seen as layers of the base for a cylinder, but not for the cone or sphere.
When radius and height are equal, one sphere will fill 2/3 of a cylinder and a cone will only take up 1/3 of a cylinder's volume. as a result this is reflected in their formulas for volume.

Vocabulary

Radius
Pi
Volume
Cylinder
Cone
Sphere

Design by Adaptive Theme