Math - 2017-18
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
- 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
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
- 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
- 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
- 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
- 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.
formula, area, perimeter, volume, polygon, circumference, closed curve,
sum, twice, length, width, height, product, pi, diameter, radius, relationship,
surface dimension, base