SIGN IN VERSION - Volume and Surface Area Word Problems - Second Set

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DENSITY = weight per cubic unit. Examples.

• Item weighing 50 pounds and taking up 100 cubic cm, has a density of 50/100 or 0.5 pounds/cm.
• Item weighing 76 pounds and taking up 100 cubic cm, has a density of 76/100 or 0.76 pounds/cm.
• Item weighing 300 grams and taking up 13 cubic in, has a density of 300/12 or 23.08 grams/in.

HEXAGON using only a side: Area = 2.6 s2 or 3√3s2 / 2

See picture for explanation. (If calculating on your own, you may use 1.73 as an approximation for √3 or 2.6 as an approximation for 3√3 / 2 .)

A hexagon is made of 6 EQUILATERAL triangles. Half of one of these triangles will be a 30/60/90 triangle. Thus we can use what we know about 30/60/90 triangles to come up with the area for this triangle and eventually the area for the hexagon.

NOTES ABOUT PRISMS BASE AREAS, Surface Areas, and Volumes

A right prism is a solid in which the sides are perpendicular to the base.

The Area formulas are as follows:

• Triangle = 1/2 x base x height
• Rectangle = length x width
• Square = side x side
• Regular Polygon = 1/2 x apothem x side x number of sides
• Circle = pi x radius squared   (use 3.14 for pi)

The Volume for any right prism (a cylinder is a right prism) is:

• The area of the base x the altitude

The Total Surface Area for any right prism (a cylinder is a right prism) is the sum of:

• The area of the bottom (base)
• The area of the top
• The area of all the sides (often called the lateral area)

A more convenient formula for the Total Surface Area = (2 x area base) + (perimeter base x altitude)

ASSUMPTIONS:

Assume that the dimensions are for the "inside" of the solid objects. The outside dimensions could be given and the thickness of the faces but this would further complicate the problems.

If no weight is given for the object, assume you only have to calculate the weight of the filling substance.

HINT FOR RIGHT TRIANGLE BASE: Use pythagorean theorem to figure out hypotenuse. Must know this side to find surface area!!!!