#### Math - 2017-18

# G.13 and *G.13 - Surface Area and Volume

**G.13** The student will **use
**formulas for surface area and volume of three-dimensional objects to **solve
**real-world problems.

G.13The student willusesurface area and volume of three-dimensional objects tosolvepractical problems.

**Bloom's Level:** Analyze

*Adopted: 2009*

### BIG IDEAS

- I can order the square feet of canvas required to make a
tent, determine how many jelly beans fill a canister, figure how much paint
will cover walls, ceiling and floor of a room, and know how much water will fill
a fish aquarium.

- I will be
able to determine when volume and surface area are appropriate for various
situations.

### UNDERSTANDING THE STANDARD

- The surface area of a three-dimensional object
is the sum of the areas of all its faces.
- The volume of a three-dimensional object is the
number of unit cubes that would fill the object.

· The surface area of a cylinder, cone, or hemisphere is the sum of the areas of the curved surface and bases.

· The surface area of a sphere is the area of the curved surface.

· The lateral area of a cylinder is the area of the curved surface of the cylinder, not including the parallel bases.

· The lateral area of a rectangular-based prism is the sum of the areas of all faces, not including the parallel bases.

· The lateral area of a triangular-based prism is the sum of the areas of all faces, not including the triangular-shaped, parallel bases.

· The volume of a three-dimensional figure is the number of unit cubes that would fill the figure.

· Composite figures consist of two or more three-dimensional figures. The surface area of a composite figure may not be equal to the sum of the surface areas of the individual figures.

· Volume and surface area of spheres, cones and cylinders should be considered in terms of p or as a decimal approximation.

· Calculators may be used to determine decimal approximations for results.### ESSENTIALS

G.13_{1} **Find**
the total surface area of cylinders, prisms, pyramids, cones, and spheres, using
the appropriate formulas.

·
G.13_{1} **Determine**
the surface area of cylinders, prisms, pyramids, cones, hemispheres, and
spheres, using the appropriate formulas.

G.13_{2}
**Calculate** the volume of cylinders,
prisms, pyramids, cones, and sphere using the appropriate formulas.

·
G.13_{2} **Determine**
the volume of cylinders, prisms, pyramids, cones, hemispheres, and spheres, using
the appropriate formulas.

G.13_{3} **Solve**
problems including real-world problems involving total surface area and volume
of cylinders, prisms, pyramids, cones and spheres as well as combinations of 3D
figures.

·
G.13_{3} **Solve**
problems including practical problems, involving surface area and volume of
cylinders, prisms, pyramids, cones, hemispheres, and spheres, as well as
composite three-dimensional figures.

·
G.13_{4} **Solve**
problems, including practical problems, involving the lateral area of circular
cylinders, prisms, and regular pyramids.

·
G.13_{5} Given information about a three-dimensional
figure such as length of a side, area of a face, or volume, **determine** missing information.

### KEY VOCABULARY

formula,
surface area, volume, three-dimensional object, height, length, slant height,
lateral area, side, lateral face, lateral edge, radius, cylinder, prism,
pyramid, cone, sphere, hemisphere, regular, polygon, parallelogram, decimal
approximation, sum, units, units squared, units cubed, net

*Updated: Oct 27, 2017*