Answer:
C. Height = 4cm, base length = 10cm, base width = 4cm
Step-by-step explanation:
A rectangular prism has
1) Base area [tex]=\text{Base Length}\times \text{Base Width}[/tex]
2) Volume [tex]= \text{Base area}\times \text{Height}[/tex]
Consider all options:
A.
[tex]\text{Base area}=10\times 4=40\ cm^2 \\ \\\text{Volume}= 40\times 2=80\ cm^3\neq 160\ cm^3[/tex]
This option is false.
B.
[tex]\text{Base area}=4\times 4=16\ cm^2\neq 40\ cm^2 \\ \\\text{Volume}= 16\times 4=64\ cm^3\neq 160\ cm^3[/tex]
This option is false.
C.
[tex]\text{Base area}=10\times 4=40\ cm^2 \\ \\\text{Volume}= 40\times 4=160\ cm^3[/tex]
This option is true.
D.
[tex]\text{Base area}=4\times 4=16\ cm^2 \neq 40\ cm^2 \\ \\\text{Volume}= 16\times 10=160\ cm^3[/tex]
This option is false.
Answer:
The rectangular prism has " Height = 4 cm, base length = 10 cm, base width 4 cm " ⇒ C
Step-by-step explanation:
The formula of the volume of a rectangular prism is V = l × w × h , where l is its length, w is its width and h is its height
∵ The area of the base of the prism is 40 cm²
∵ The its base is shaped a rectangle
∵ Area of a rectangle = l × w
∴ l × w = 40 cm²
∵ The volume of the prism is 160 cm³
- Substitute l × w and the volume in the formula of the volume
∴ 160 = 40 × h
- Divide both sides by 40
∴ 4 = h
∴ The length of the height of the prism is 4 cm
- Lets find which two numbers give a product of 40 to find l and w
∵ 40 = 10 × 4
∴ l = 10 cm and w = 4 cm
The rectangular prism has " Height = 4 cm, base length = 10 cm, base width 4 cm"
