MLS Yolanda
Volcimus
Harvard 3/16/13
Throughout my exploration of volume, I have learned about
different relationships of shapes and I had an understanding of these
relationships that helped me to remember the formulas used to find each figures
volume. I have learned the different uses for the formula V = BH. I learned the
relationship between rectangular prisms and square pyramids. Also, I’ve learned
the relationship between triangular prisms and triangular pyramids. Lastly, I
was able to tell the relationship between cylinders and cones. Therefore, I
have learned numerous different associations of figures and by using these
relationships, I was able to remember the formula of each shapes’ volume.
There are several different uses of the formula V = BH. For
example, we used the formula V = BH for a cylinder, a rectangular prism, and a triangular
pyramid. However, the formula does change depending on the shape I am determine
to find the volume of. For example, to find the volume of a cylinder, we use
the formula V = BH. To find the value of B, we use the formula B = π r2 because the base of a cylinder is a circle
and in order to find the volume of the cylinder, we must find the area of that
circle. In addition, when we find the volume of a rectangular prism, we also
use the formula V = BH. However, we find the B by using the formula B = LW
because the base of a rectangular prism is a rectangle and we must find the
area of the rectangle first before finding the volume of the whole figure. Lastly,
we also use the formula V = BH to find the volume of a triangular pyramid. In
the other hand, to find the B, we use the formula B = ½ bh. We use this formula
to find B because the base of a triangular pyramid is a triangle and we must
find the area of the triangle first which is ½ bh before finding the volume of
the whole triangular prism. That is to say, there are various ways we can use
the formula V = BH to find the volume of many shapes and each shapes has a
different used of the B.
A rectangular prism is a 3-d shape that has six faces which are
all rectangles. A square pyramid is a pyramid with a square base. The relationship between a
rectangular prism and a square pyramid is that a square pyramid is 1/3 of a
rectangular prism. The formula used to determine the volume of a rectangular
prism is V = BH where B would be represented by the formula B = bh. However,
the formula that we use to find the volume of a square pyramid is 1/3 BH. The
formula has 1/3 in it because three square pyramids make one rectangular with
the same Base and Height. The relationship between these two shapes helps me to
remember and understand the formulas used for determining their volumes because
since I know that a square pyramid id=s 1/3 of a rectangular, I know that a
square pyramid’s volume formula will have 1/3 in front of it. In addition, I
also know that to find the volume any prisms or pyramid, I need to multiply the
Base by the Height. That is to say, rectangular prisms and square pyramids have
a special relationship which helps me to remember the formula of finding their
volumes.
A triangular prism is a prism whose base is a triangle.
Nevertheless, a triangular pyramid is a pyramid with a base of a rectangle. The
relationship between a triangular prism and a triangular pyramid is a
triangular pyramid is 1/3 of a triangular prism. The formula that is used to
determine the volume of a triangular prism is V = BH where B would be
represented by the formula B = ½ bh. On
the other hand, the formula for the volume of a triangular pyramid is V =
1/3BH. In this formula, B would also be represented by the formula B = ½ bh.
The relationship between these two shapes helps me to remember and understand
the formulas used for determining their volume because I know that three triangular
prisms will make one triangular pyramid with the same height and base. This
also means that the volume formula of a triangular pyramid will also have 1/3
in front of it. That is to say, the relationship between a triangular prism and
a triangular pyramid is that a triangular prism is 1/3 of a triangular prism.
A cylinder is a geometry shape with straight parallel sides and a circle
for a base. However, a cone is a solid that has a circular base and only one apex. A cone
is also considered a pyramid with infinite amount of faces. The relation
between a cylinder and a cone is that a cone is 1/3 (one-third) of a cylinder. The
formula that is used to find the volume of a cylinder is V = π r2h. Conversely, the formula that is used to
determine the volume of a cone is V = 1/3 π r2h.
The relationship between these two shapes help me remember and understand the
formula used for determining their volume because since I now know that that
three cones will equal to one cylinder with the same height and base, I know
the volume formula of a cone will contain 1/3 in front of it. Also, I know that
the area of any circle is represented by the formula A = π r2h which means when we find the volume of these two
figures, we actually finding the area of their bases and multiplying it be the
height. In conclusion, the relationship between a cone and a cylinder is that a
cylinder is three times a cone.
To wrap it all up, over the last two weeks in my exploration of volume, I have learned about different relationship of shapes and how they are related to one another. Moreover, I learned that there are various used of the formula V = BH. Also, I learned that a square pyramid is equal to 1/3 of a rectangular prism with same base and height. In addition, a triangular prism is 1/3 of a triangular prism. Lastly, three cones are equal to one cylinder that has the same height and base with the cone. In conclusion, throughout these two weeks, I have learned several different relationships between several different shapes.
