# 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.13  The student will use surface area and volume of three-dimensional objects to solve practical problems.

Bloom's Level:  Analyze

### 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.131  Find the total surface area of cylinders, prisms, pyramids, cones, and spheres, using the appropriate formulas.

·  G.131  Determine the surface area of cylinders, prisms, pyramids, cones, hemispheres, and spheres, using the appropriate formulas.

G.132  Calculate the volume of cylinders, prisms, pyramids, cones, and sphere using the appropriate formulas.

·  G.132  Determine the volume of cylinders, prisms, pyramids, cones, hemispheres, and spheres, using the appropriate formulas.

G.133  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.133  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.134  Solve problems, including practical problems, involving the lateral area of circular cylinders, prisms, and regular pyramids.

·  G.135  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