# 6.10d - Volume and Surface Area

6.10d    The student will

d) describe and determine the volume and surface area of a rectangular prism.

Bloom's Level:  Remember, Apply

### BIG IDEAS

• I can make a tent by determining the square feet of canvas needed for 4 walls and floor, how much netting is needed for the door, and how long a zipper will surround the door opening.
• I will be able to find area, perimeter, circumference, and surface area as appropriate in various situations.

### UNDERSTANDING THE STANDARD

• Experiences in deriving the formulas for area, perimeter, and volume using manipulatives such as tiles, one-inch cubes, adding machine tape, graph paper, geoboards, or tracing paper, promote an understanding of the formulas and facility in their use.†
• The perimeter of a polygon is the measure of the distance around the polygon.
• Circumference is the distance around or perimeter of a circle.
• The area of a closed curve is the number of nonoverlapping square units required to fill the region enclosed by the curve.
• The perimeter of a square whose side measures s is 4 times s (P = 4s), and its area is side times side  (A = s2).
• The perimeter of a rectangle is the sum of twice the length and twice the width [P = 2l + 2w, or P = 2(l + w)], and its area is the product of the length and the width (A = lw).
• The value of pi (π) is the ratio of the circumference of a circle to its diameter.
• The ratio of the circumference to the diameter of a circle is a constant value, pi (π), which can be approximated by measuring various sizes of circles.
• The fractional approximation of pi generally used is 22/7.
• The decimal approximation of pi generally used is 3.14.
• The circumference of a circle is computed using C = πd or C = 2πr, where d is the diameter and r is the radius of the circle.
• The area of a circle is computed using the formula , A = πr2 where r is the radius of the circle.
• The surface area of a rectangular prism is the sum of the areas of all six faces (SA = 2lw + 2lh + 2wh).
• The volume of a rectangular prism is computed by multiplying the area of the base, B, (length x width) by the height of the prism (V = lwh = Bh).

†Revised March 2011

### ESSENTIALS

• What is the relationship between area and surface area?  Surface area is calculated for a three-dimensional figure. It is the sum of the areas of the two-dimensional surfaces that make up the three-dimensional figure.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

6.10d1 Solve problems that require finding the surface area of a rectangular prism given a diagram of the prism with the necessary dimensions labeled.

6.10d2 Solve problems that require finding the volume of a rectangular prism given a diagram of the prism with the necessary dimensions labeled.

### KEY VOCABULARY

formula, area, perimeter, volume, polygon, circumference, closed curve, sum, twice, length, width, height, product, pi, diameter, radius, relationship, surface dimension, base

Updated: Jun 05, 2017