MATHEMATICS MIDDLE SCHOOL

Which of these rectangular prisms has a base area of 40cm2 and a volume of 160cm3?A. Height = 2cm, base length = 10cm, base width = 4cm
B. Height = 4cm, base length = 4cm, base width = 4cm
C. Height = 4cm, base length = 10cm, base width = 4cm
D. Height = 10cm, base length = 4cm, base width = 4cm

Answers

Answer 1
Answer:

Answer:

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

Step-by-step explanation:

A rectangular prism has

1) Base area =\text{Base Length}* \text{Base Width}

2) Volume = \text{Base area}* \text{Height}

Consider all options:

A.

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

This option is false.

B.

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

This option is false.

C.

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

This option is true.

D.

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

This option is false.
Answer 2
Answer:

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"

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Answers

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Answers

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