Question

Which of these rectangular prisms has a base area of 40cm2 and a volume of 160cm3?

Answer 1

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"

Answer 2

Answer:

C. Height = 4cm, base length = 10cm, base width = 4cm

Step-by-step explanation:

A rectangular prism has

1) Base area $=\text{Base Length}\times \text{Base Width}$

2) Volume $= \text{Base area}\times \text{Height}$

Consider all options:

A.

$\text{Base area}=10\times 4=40\ cm^2 \\ \\\text{Volume}= 40\times 2=80\ cm^3\neq 160\ cm^3$

This option is false.

B.

$\text{Base area}=4\times 4=16\ cm^2\neq 40\ cm^2 \\ \\\text{Volume}= 16\times 4=64\ cm^3\neq 160\ cm^3$

This option is false.

C.

$\text{Base area}=10\times 4=40\ cm^2 \\ \\\text{Volume}= 40\times 4=160\ cm^3$

This option is true.

D.

$\text{Base area}=4\times 4=16\ cm^2 \neq 40\ cm^2 \\ \\\text{Volume}= 16\times 10=160\ cm^3$

This option is false.