Answer:SA= 3 ∗ 3 ∗ 6 =36 cm^2
Cylinders
Understand the Formula –Many times students think it is enough to remember and know how to apply a formula.
They do no see why it is necessary to understand how and why it works. The benefit of fully understanding what
the formula is doing is versatility. Substituting and simplifying works wonderfully for standard cylinders, but what
if the surface area of a composite solid needs to be found.
Key Exercise:
- Find the surface area of the piece of pipe illustrated in the composite solid part of this section.
Answer:A= 2 B+L= 2 ∗(π 32 +π 22 )+ 2 π∗ 3 ∗ 5 = 56 πcm^2 ≈ 176 .9 cm^2
Make and Take Apart a Cylinder –Students have a difficult time understanding that the length of the rectangle
that composes the lateral area of a cylinder has length equal to the circumference of the circular base. First, review
the definition of circumference with the students. A good way to describe the circumference is to talk about an ant
walking around the circle. Next, let them play with some paper cylinders. Have them cut out circular bases, and
then fit a rectangle to the circles to make the lateral surface. After some time spent trying to tape the rectangle to the
circle, they will understand that the length of the rectangle matches up with the outside of the circle, and therefore,
must be the same as the circumference of the circle.
The Volume Base –In the past, when students used formulas, they just needed to identify the correct number to
substitute in for each variable. Calculating a volume requires more steps. To find the correct value to substitute
into theBin the formulaV=Bh, usually requires doing a calculation with an area formula. Students will often
forget this step, and use the length of the base of the polygon that is the base of the prism for theB. Emphasize
the difference betweenb, the linear measurement of the length of a side of a polygon, andB, the area of the two-
dimensional polygon that is the base of the prism. Students can use dimensional analysis to check their work.
Volume is measured in cubic units, so three linear measurements, or a linear unit and a squared unit must be fed into
the formula.
Additional Exercises:
- The volume of a 4 in tall coffee cup is approximately 50 in^3. What is the radius of the base of the cup?
Answer:
50 =πr^2 ∗ 4 The cup has a radius of approximately 2 inches.
r≈ 2Pyramids
Don’t Forget the^13 – The most common mistake students make when calculating the volume of a pyramid is to
forget to divide by three. They also might mistakenly divide by three when trying to find the volume of a prim. The
first step students should take when beginning a volume calculation, is to make the decision if the solid is a prism or
a pyramid. Once they have chosen, they should immediately write down the correct volume formula.
Prism or Pyramid –Some students have trouble deciding if a solid is a prism or a pyramid. Most try to make the
determination by looking for the bases. This is especially tricky if the figure is not sitting on its base. Another method
for differentiating between these solids is to look at the lateral faces. If there are a large number of parallelograms,
2.11. Surface Area and Volume