Answer:
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
Step-by-step explanation:
To solve this problem calculate the volume of each solid
case A) A cube with edge 5 cm
The volume of a cube is equal to
[tex]V=b^{3}[/tex]
where
b is the length side of the cube
substitute the value
[tex]V=5^{3}=125\ cm^{3}[/tex]
case B) A cylinder with radius 4 cm and height 4 cm
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
substitute the value
[tex]V=(3.14)(4)^{2} (4)=200.96\ cm^{3}[/tex]
case C) A square pyramid with base edges 6 cm and height 6 cm
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
Find the area of the base B
[tex]B=6^{2}=36\ cm^{2}[/tex] ----> is a square
substitute the values
[tex]V=\frac{1}{3}(36)(6)=72\ cm^{3}[/tex]
case D) A cone with radius 4 cm and height 9 cm
The volume of a cone is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the cone
Find the area of the base B
[tex]B=\pi r^{2}=(3.14)(4^{2})=50.24\ cm^{2}[/tex] ----> is a circle
substitute the values
[tex]V=\frac{1}{3}(50.24)(9)=150.72\ cm^{3}[/tex]
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(5)(5)(6)=150\ cm^{3}[/tex]
therefore
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
