Use formula for the volume of a prism and for the volume of a cylinder.
C
c
Use formula for the volume of a prism and for the volume of a cylinder.
A
a
Example Possible Dimensions: Length 2 inches, width 2 inches, height 15Ï€ inches
B
b
Example Possible Dimensions: Base side length 1 inch, height 60Ï€ inches
C
c
Example Possible Dimensions: Lengths of the legs of the base 1 inch, height 120Ï€ inches
Practice makes perfect
a
A cylindrical can is modeled by the following cylinder with a radius of r=2 inches and a height of h=5 inches.
It takes three full cans to fill a container. First, let's find the volume of the can. We know that the volume of the container is three times the volume of the can. We will use the formula for the volume of a cylinder.
Therefore, the volume of the can is 20Ï€ cubic inches. This tells us that the volume of the container is 3* 20Ï€=60Ï€ cubic inches.
V_\text{container}=60\pi cubic inches.
We are asked to find possible dimensions of the container if it is in a shape of a rectangular prism. Let l, w, and h represent the dimensions of this prism.
The volume of a rectangular prism is the product of its dimension. This tells us that V_\text{container}=\ell w h.
Therefore, the possible dimensions of the container are l= 2, w= 2, and h= 15Ï€ inches. Remember that there are many ways to factor the number 60Ï€ and this is just one possible solution.
b
From Part A we know that the volume of a container is 60Ï€ cubic inches. We are asked to find possible dimensions of the container if it is in a shape of a square prism. Let s be the side length of the base and h be the height of the prism.
The volume of a rectangular prism is the product of its dimension. This tells us that V_\text{container}=s\cdot s\cdot h.
Therefore, the possible dimensions of the container are s= 1 and h= 60Ï€ inches. Remember that there are many ways to factor the number 60Ï€.
c
From Part A we know that the volume of a container is 60Ï€ cubic inches. We are asked to find possible dimensions of the container if it is in a shape of a triangular prism with a right triangle as the base. Let a and b be the lengths of the legs of the base and h be the height of the prism.
Since the base is a right triangle, its area is the half of the product of its legs. This tells us that B= ab2. By the formula for the volume of a prism, we get that V_\text{container}=Bh=\frac{ab}{2}h.
