Question

select the two correct answers.
a right rectangular prism has a volume of 40 cubic feet.
$v = l \times w \times h$ or $v = b \times h$
which sets of measurements could describe this right rectangular prism?

• base area of 80 square feet and height of 2 feet
• base area of 10 square feet and height of 4 feet
• length of 15 feet, width of 20 feet, and height of 5 feet
• length of 2 feet, width of 4 feet, and height of 5 feet
• base area of 30 square feet and height of 10 feet
• length of 5 feet, width of 4 feet, and height of 20 feet

Explanation:

Step1: Check the first option

Using the formula \( V = b\times h \), where \( b = 80 \) square feet and \( h = 2 \) feet.
\( V = 80\times2 = 160 \) cubic feet. Not equal to 40. So this option is wrong.

Step2: Check the second option

Using \( V = b\times h \), \( b = 10 \) square feet, \( h = 4 \) feet.
\( V = 10\times4 = 40 \) cubic feet. This works.

Step3: Check the third option

Using \( V = l\times w\times h \), \( l = 15 \), \( w = 20 \), \( h = 5 \).
\( V = 15\times20\times5 = 1500 \) cubic feet. Not 40. Wrong.

Step4: Check the fourth option

Using \( V = l\times w\times h \), \( l = 2 \), \( w = 4 \), \( h = 5 \).
\( V = 2\times4\times5 = 40 \) cubic feet. This works.

Step5: Check the fifth option

Using \( V = b\times h \), \( b = 30 \), \( h = 10 \).
\( V = 30\times10 = 300 \) cubic feet. Wrong.

Step6: Check the sixth option

Using \( V = l\times w\times h \), \( l = 5 \), \( w = 4 \), \( h = 20 \).
\( V = 5\times4\times20 = 400 \) cubic feet. Wrong.

Answer:

B. Base area of 10 square feet and height of 4 feet
D. Length of 2 feet, width of 4 feet, and height of 5 feet